Arthur parameters and cuspidal automorphic modules of classical groups

Dihua Jiang; Lei Zhang

doi:https://doi.org/10.4007/annals.2020.191.3.2

Abstract

The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks how to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In this paper, we formulate a general construction of concrete modules, using Bessel periods, for cuspidal automorphic representations of classical groups with generic global Arthur parameters. Then we establish the theory for orthogonal and unitary groups, based on certain well expected conjectures. Among the consequences of the theory in this paper is that the global Gan-Gross-Prasad conjecture for those classical groups is proved in full generality in one direction and with a global assumption in the other direction.

Show/hide bibliography for this article

[ABV] $Go to document$ J. Adams, D. Barbasch, and D. A. Vogan Jr., The Langlands Classification and Irreducible Characters for Real Reductive Groups, Birkhäuser Boston, Inc., Boston, MA, 1992, vol. 104.

Show bibtex

@BOOK{ABV, author = {Adams, Jeffrey and Barbasch, Dan and Vogan, Jr., David A.}, title = {The {L}anglands Classification and Irreducible Characters for Real Reductive Groups}, series = {Progr. Math.}, volume = {104}, publisher = {Birkhäuser Boston, Inc., Boston, MA}, year = {1992}, pages = {xii+318}, isbn = {0-8176-3634-X}, mrclass = {22-02 (22E47)}, mrnumber = {1162533}, mrreviewer = {Brian E. Blank}, doi = {10.1007/978-1-4612-0383-4}, url = {https://doi.org/10.1007/978-1-4612-0383-4}, zblnumber = {0756.22004}, }
[AGRS] $Go to document$ A. Aizenbud, D. Gourevitch, S. Rallis, and G. Schiffmann, "Multiplicity one theorems," Ann. of Math. (2), vol. 172, iss. 2, pp. 1407-1434, 2010.

Show bibtex

@ARTICLE{AGRS, author = {Aizenbud, Avraham and Gourevitch, Dmitry and Rallis, Stephen and Schiffmann, Gérard}, title = {Multiplicity one theorems}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {172}, year = {2010}, number = {2}, pages = {1407--1434}, issn = {0003-486X}, mrclass = {22E50 (20G05)}, mrnumber = {5}, mrreviewer = {Christian A. Zorn}, doi = {10.4007/annals.2010.172.1413}, url = {https://doi.org/10.4007/annals.2010.172.1413}, zblnumber = {1202.22012}, }
[A13] $Go to document$ J. Arthur, The Endoscopic Classification of Representations, Amer. Math. Soc., Providence, RI, 2013, vol. 61.

Show bibtex

@BOOK{A13, author = {Arthur, James}, title = {The Endoscopic Classification of Representations}, series = {Amer. Math. Soc. Colloq. Publ.}, volume = {61}, note = {Orthogonal and symplectic groups}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2013}, pages = {xviii+590}, isbn = {978-0-8218-4990-3}, mrclass = {22E55 (11F66 11F70 11F72 11R37 20G25 22E50)}, mrnumber = {3135650}, mrreviewer = {Dihua Jiang}, doi = {10.1090/coll/061}, url = {https://doi.org/10.1090/coll/061}, zblnumber = {1310.22014}, }
[A-P5] J. Arthur, "Characters and modules," in Representation Theory, Automorphic Forms & Complex Geometry. A Tribute to W. Schmid, International Press, Somerville, MA, 2020, pp. 15-16.

Show bibtex

@INCOLLECTION{A-P5, author = {Arthur, James}, title = {Characters and modules}, booktitle = {Representation Theory, Automorphic Forms \& Complex Geometry. A Tribute to W. Schmid}, year = {2020}, pages = {15--16}, publisher = {International Press, Somerville, MA}, zblnumber = {}, }
[AG] $Go to document$ H. Atobe and W. T. Gan, "On the local Langlands correspondence and Arthur conjecture for even orthogonal groups," Represent. Theory, vol. 21, pp. 354-415, 2017.

Show bibtex

@ARTICLE{AG, author = {Atobe, Hiraku and Gan, Wee Teck}, title = {On the local {L}anglands correspondence and {A}rthur conjecture for even orthogonal groups}, journal = {Represent. Theory}, fjournal = {Representation Theory. An Electronic Journal of the Amer. Math. Soc.}, volume = {21}, year = {2017}, pages = {354--415}, mrclass = {11F70 (11R39)}, mrnumber = {3708200}, mrreviewer = {Kimball L. Martin}, doi = {10.1090/ert/504}, url = {https://doi.org/10.1090/ert/504}, zblnumber = {1419.11088}, }
[BAS1] $Go to document$ A. Ben-Artzi and D. Soudry, "$L$-functions for ${ U}_m\times R_{E/F}{ GL}_n (n\leq[{m\over2}])$," in Automorphic Forms and $L$-Functions I. Global Aspects, Amer. Math. Soc., Providence, RI, 2009, vol. 488, pp. 13-59.

Show bibtex

@INCOLLECTION{BAS1, author = {Ben-Artzi, Asher and Soudry, David}, title = {{$L$}-functions for {${\rm U}_m\times R_{E/F}{\rm GL}_n (n\leq[{m\over2}])$}}, booktitle = {Automorphic Forms and {$L$}-Functions {I}. {G}lobal Aspects}, series = {Contemp. Math.}, volume = {488}, pages = {13--59}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2009}, mrclass = {11F66 (11F70)}, mrnumber = {2522026}, mrreviewer = {Anton Deitmar}, doi = {10.1090/conm/488/09563}, url = {https://doi.org/10.1090/conm/488/09563}, zblnumber = {1187.11018}, }
[BAS2] $Go to document$ A. Ben-Artzi and D. Soudry, "On $L$-functions for ${ U}_{2k}\times{ R}_{E/F}{ GL}_m$, $(k<m)$," in Advances in the Theory of Automorphic Forms and their $L$-Functions, Amer. Math. Soc., Providence, RI, 2016, vol. 664, pp. 69-104.

Show bibtex

@INCOLLECTION{BAS2, author = {Ben-Artzi, Asher and Soudry, David}, title = {On {$L$}-functions for {${\rm U}_{2k}\times{\rm R}_{E/F}{\rm GL}_m$}, {$(k booktitle = {Advances in the Theory of Automorphic Forms and their {$L$}-Functions}, series = {Contemp. Math.}, volume = {664}, pages = {69--104}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2016}, mrclass = {11F70 (22E30 22E35)}, mrnumber = {3502977}, mrreviewer = {Pramod Kumar Kewat}, doi = {10.1090/conm/664/13039}, url = {https://doi.org/10.1090/conm/664/13039}, zblnumber = {1418.11086}, }
[BP12] $Go to document$ R. Beuzart-Plessis, "La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes unitaires," Mém. Soc. Math. Fr. (N.S.), iss. 149, p. vii, 2016.

Show bibtex

@ARTICLE{BP12, author = {Beuzart-Plessis, Raphaël}, title = {La conjecture locale de {G}ross-{P}rasad pour les représentations tempérées des groupes unitaires}, journal = {Mém. Soc. Math. Fr. (N.S.)}, fjournal = {Mémoires de la Société Mathématique de France. Nouvelle Série}, year = {2016}, number = {149}, pages = {vii+191}, issn = {0249-633X}, isbn = {978-2-85629-841-1}, mrclass = {22E45 (11F70 11F85 20G05)}, mrnumber = {3676153}, mrreviewer = {O. V. Shvartsman}, doi = {10.24033/msmf.457}, url = {https://doi.org/10.24033/msmf.457}, zblnumber = {1357.22008}, }
[BP] R. Beuzart-Plessis, A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the Archimedean case, 2015.

Show bibtex

@misc{BP, author = {Beuzart-Plessis, R.}, title={A local trace formula for the {G}an-{G}ross-{P}rasad conjecture for unitary groups: the {A}rchimedean case}, arxiv={1506.01452}, year={2015}, }
[BW] $Go to document$ A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, Second ed., Amer. Math. Soc., Providence, RI, 2000, vol. 67.

Show bibtex

@BOOK{BW, author = {Borel, A. and Wallach, N.}, title = {Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups}, series = {Math. Surv. Monog.}, volume = {67}, edition = {Second}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2000}, pages = {xviii+260}, isbn = {0-8218-0851-6}, mrclass = {22E41 (22-02 22E40 22E45 57T15)}, mrnumber = {1721403}, mrreviewer = {F. E. A. Johnson}, doi = {10.1090/surv/067}, url = {https://doi.org/10.1090/surv/067}, zblnumber = {0980.22015}, }
[CKPSS04] $Go to document$ J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, "Functoriality for the classical groups," Publ. Math. Inst. Hautes Études Sci., iss. 99, pp. 163-233, 2004.

Show bibtex

@ARTICLE{CKPSS04, author = {Cogdell, J. W. and Kim, H. H. and Piatetski-Shapiro, I. I. and Shahidi, F.}, title = {Functoriality for the classical groups}, journal = {Publ. Math. Inst. Hautes \'{E}tudes Sci.}, fjournal = {Publications Mathématiques. Institut de Hautes \'{E}tudes Scientifiques}, number = {99}, year = {2004}, pages = {163--233}, issn = {0073-8301}, mrclass = {22E46 (22E55)}, mrnumber = {2075885}, doi = {10.1007/s10240-004-0020-z}, url = {https://doi.org/10.1007/s10240-004-0020-z}, zblnumber = {1090.22010}, }
[D-M] J. Dixmier and P. Malliavin, "Factorisations de fonctions et de vecteurs indéfiniment différentiables," Bull. Sci. Math. (2), vol. 102, iss. 4, pp. 307-330, 1978.

Show bibtex

@ARTICLE{D-M, author = {Dixmier, Jacques and Malliavin, Paul}, title = {Factorisations de fonctions et de vecteurs indéfiniment différentiables}, journal = {Bull. Sci. Math. (2)}, fjournal = {Bulletin des Sciences Mathématiques. 2e Série}, volume = {102}, year = {1978}, number = {4}, pages = {307--330}, issn = {0007-4497}, mrclass = {22E30}, mrnumber = {0517765}, mrreviewer = {Mitsuo Sugiura}, zblnumber = {0392.43013}, }
[FM] $Go to document$ M. Furusawa and K. Morimoto, "On special Bessel periods and the Gross-Prasad conjecture for ${ SO}(2n+1)\times{ SO}(2)$," Math. Ann., vol. 368, iss. 1-2, pp. 561-586, 2017.

Show bibtex

@ARTICLE{FM, author = {Furusawa, Masaaki and Morimoto, Kazuki}, title = {On special {B}essel periods and the {G}ross-{P}rasad conjecture for {${\rm SO}(2n+1)\times{\rm SO}(2)$}}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {368}, year = {2017}, number = {1-2}, pages = {561--586}, issn = {0025-5831}, mrclass = {11F55 (11F27 11F46 11F67 22E50 22E55)}, mrnumber = {3651583}, mrreviewer = {Ian Whitehead}, doi = {10.1007/s00208-016-1440-z}, url = {https://doi.org/10.1007/s00208-016-1440-z}, zblnumber = {1398.11078}, }
[Gan-AMV] $Go to document$ W. T. Gan, "Recent progress on the Gross-Prasad conjecture," Acta Math. Vietnam., vol. 39, iss. 1, pp. 11-33, 2014.

Show bibtex

@ARTICLE{Gan-AMV, author = {Gan, Wee Teck}, title = {Recent progress on the {G}ross-{P}rasad conjecture}, journal = {Acta Math. Vietnam.}, fjournal = {Acta Mathematica Vietnamica}, volume = {39}, year = {2014}, number = {1}, pages = {11--33}, issn = {0251-4184}, mrclass = {11F70 (11F67)}, mrnumber = {3176460}, mrreviewer = {Neven Grbac}, doi = {10.1007/s40306-014-0047-2}, url = {https://doi.org/10.1007/s40306-014-0047-2}, zblnumber = {1325.11045}, }
[GGP12] W. T. Gan, B. H. Gross, and D. Prasad, "Symplectic local root numbers, central critical $L$ values, and restriction problems in the representation theory of classical groups," in Sur les Conjectures de Gross et Prasad. I, Math. Soc. France, Paris, 2012, vol. 346, pp. 1-109.

Show bibtex

@INCOLLECTION{GGP12, author = {Gan, Wee Teck and Gross, Benedict H. and Prasad, Dipendra}, title = {Symplectic local root numbers, central critical {$L$} values, and restriction problems in the representation theory of classical groups}, booktitle = {Sur les Conjectures de Gross et Prasad. I}, series = {Astérisque}, volume = {346}, publisher = {Math. Soc. France, Paris}, year = {2012}, pages = {1--109}, issn = {0303-1179}, isbn = {978-2-85629-348-5}, mrclass = {22E50 (11F70 11R39 22E55)}, mrnumber = {3202556}, zblnumber = {1280.22019}, }
[GGP] W. T. Gan, B. H. Gross, and D. Prasad, "Restrictions of representations of classical groups: examples," in Sur les Conjectures de Gross et Prasad. I, Math. Soc. France, Paris, 2012, vol. 346, pp. 111-170.

Show bibtex

@INCOLLECTION{GGP, author = {Gan, Wee Teck and Gross, Benedict H. and Prasad, Dipendra}, title = {Restrictions of representations of classical groups: examples}, booktitle = {Sur les Conjectures de Gross et Prasad. I}, journal = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {346}, year = {2012}, pages = {111--170}, issn = {0303-1179}, isbn = {978-2-85629-348-5}, mrclass = {22E50 (11F70 11R39 22E55)}, mrnumber = {3202557}, zblnumber = {1279.22023}, }
[GGP-ng] W. T. Gan, B. H. Gross, and D. Prasad, Branching laws for classical groups: the non-tempered case, 2019.

Show bibtex

@MISC{GGP-ng, author = {Gan, Wee Teck and Gross, Benedict H. and Prasad, Dipendra}, title = {Branching laws for classical groups: the non-tempered case}, arxiv = {1911.02783v1}, year = {2019}, zblnumber = {}, }
[GI] $Go to document$ W. T. Gan and A. Ichino, "The Gross-Prasad conjecture and local theta correspondence," Invent. Math., vol. 206, iss. 3, pp. 705-799, 2016.

Show bibtex

@ARTICLE{GI, author = {Gan, Wee Teck and Ichino, Atsushi}, title = {The {G}ross-{P}rasad conjecture and local theta correspondence}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {206}, year = {2016}, number = {3}, pages = {705--799}, issn = {0020-9910}, mrclass = {11F70 (11F85 22E50)}, mrnumber = {3573972}, mrreviewer = {Ivan Matić}, doi = {10.1007/s00222-016-0662-8}, url = {https://doi.org/10.1007/s00222-016-0662-8}, zblnumber = {1358.11061}, }
[GPSR97] $Go to document$ D. Ginzburg, I. Piatetski-Shapiro, and S. Rallis, "$L$ functions for the orthogonal group," Mem. Amer. Math. Soc., vol. 128, iss. 611, p. viii, 1997.

Show bibtex

@ARTICLE{GPSR97, author = {Ginzburg, D. and Piatetski-Shapiro, I. and Rallis, S.}, title = {{$L$} functions for the orthogonal group}, journal = {Mem. Amer. Math. Soc.}, fjournal = {Memoirs of the Amer. Math. Soc.}, volume = {128}, year = {1997}, number = {611}, pages = {viii+218}, issn = {0065-9266}, mrclass = {11F70 (11F55 11F66 22E50 22E55)}, mrnumber = {1357823}, mrreviewer = {Solomon Friedberg}, doi = {10.1090/memo/0611}, url = {https://doi.org/10.1090/memo/0611}, zblnumber = {0884.11022}, }
[GJR04] $Go to document$ D. Ginzburg, D. Jiang, and S. Rallis, "On the nonvanishing of the central value of the Rankin-Selberg $L$-functions," J. Amer. Math. Soc., vol. 17, iss. 3, pp. 679-722, 2004.

Show bibtex

@ARTICLE{GJR04, author = {Ginzburg, David and Jiang, Dihua and Rallis, Stephen}, title = {On the nonvanishing of the central value of the {R}ankin-{S}elberg {$L$}-functions}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the Amer. Math. Soc.}, volume = {17}, year = {2004}, number = {3}, pages = {679--722}, issn = {0894-0347}, mrclass = {11F67 (11F70 22E46)}, mrnumber = {2053953}, mrreviewer = {Henry H. Kim}, doi = {10.1090/S0894-0347-04-00455-2}, url = {https://doi.org/10.1090/S0894-0347-04-00455-2}, zblnumber = {1057.11029}, }
[GJR05] $Go to document$ D. Ginzburg, D. Jiang, and S. Rallis, "On the nonvanishing of the central value of the Rankin-Selberg $L$-functions. II," in Automorphic Representations, $L$-Functions and Applications: Progress and Prospects, de Gruyter, Berlin, 2005, vol. 11, pp. 157-191.

Show bibtex

@INCOLLECTION{GJR05, author = {Ginzburg, David and Jiang, Dihua and Rallis, Stephen}, title = {On the nonvanishing of the central value of the {R}ankin-{S}elberg {$L$}-functions. {II}}, booktitle = {Automorphic Representations, {$L$}-Functions and Applications: Progress and Prospects}, series = {Ohio State Univ. Math. Res. Inst. Publ.}, volume = {11}, pages = {157--191}, publisher = {de Gruyter, Berlin}, year = {2005}, mrclass = {11F70 (11F67 22E55)}, mrnumber = {2192823}, mrreviewer = {Henry H. Kim}, doi = {10.1515/9783110892703.157}, url = {https://doi.org/10.1515/9783110892703.157}, zblnumber = {1115.11027}, }
[GJR09] $Go to document$ D. Ginzburg, D. Jiang, and S. Rallis, "Models for certain residual representations of unitary groups," in Automorphic Forms and $L$-Functions I. Global Aspects, Amer. Math. Soc., Providence, RI, 2009, vol. 488, pp. 125-146.

Show bibtex

@INCOLLECTION{GJR09, author = {Ginzburg, David and Jiang, Dihua and Rallis, Stephen}, title = {Models for certain residual representations of unitary groups}, booktitle = {Automorphic Forms and {$L$}-Functions {I}. {G}lobal Aspects}, series = {Contemp. Math.}, volume = {488}, pages = {125--146}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2009}, mrclass = {22E55 (11F70 11M36)}, mrnumber = {2522030}, mrreviewer = {Henry H. Kim}, doi = {10.1090/conm/488/09567}, url = {https://doi.org/10.1090/conm/488/09567}, zblnumber = {1195.11069}, }
[GRS11] $Go to document$ D. Ginzburg, S. Rallis, and D. Soudry, The Descent Map from Automorphic Representations of ${ GL}(n)$ to Classical Groups, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011.

Show bibtex

@BOOK{GRS11, author = {Ginzburg, David and Rallis, Stephen and Soudry, David}, title = {The Descent Map from Automorphic Representations of {${\rm GL}(n)$} to Classical Groups}, publisher = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ}, year = {2011}, pages = {x+339}, isbn = {978-981-4304-98-6; 981-4304-98-0}, mrclass = {22E55 (11F70)}, mrnumber = {2848523}, mrreviewer = {Erez M. Lapid}, doi = {10.1142/9789814304993}, url = {https://doi.org/10.1142/9789814304993}, zblnumber = {1233.11056}, }
[GP92] $Go to document$ B. H. Gross and D. Prasad, "On the decomposition of a representation of ${ SO}_n$ when restricted to ${ SO}_{n-1}$," Canad. J. Math., vol. 44, iss. 5, pp. 974-1002, 1992.

Show bibtex

@ARTICLE{GP92, author = {Gross, Benedict H. and Prasad, Dipendra}, title = {On the decomposition of a representation of {${\rm SO}_n$} when restricted to {${\rm SO}_{n-1}$}}, journal = {Canad. J. Math.}, fjournal = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques}, volume = {44}, year = {1992}, number = {5}, pages = {974--1002}, issn = {0008-414X}, mrclass = {22E50 (11R39 22E55)}, mrnumber = {1186476}, mrreviewer = {David Joyner}, doi = {10.4153/CJM-1992-060-8}, url = {https://doi.org/10.4153/CJM-1992-060-8}, zblnumber = {0787.22018}, }
[GP94] $Go to document$ B. H. Gross and D. Prasad, "On irreducible representations of ${ SO}_{2n+1}\times{ SO}_{2m}$," Canad. J. Math., vol. 46, iss. 5, pp. 930-950, 1994.

Show bibtex

@ARTICLE{GP94, author = {Gross, Benedict H. and Prasad, Dipendra}, title = {On irreducible representations of {${\rm SO}_{2n+1}\times{\rm SO}_{2m}$}}, journal = {Canad. J. Math.}, fjournal = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques}, volume = {46}, year = {1994}, number = {5}, pages = {930--950}, issn = {0008-414X}, mrclass = {22E50 (11S37)}, mrnumber = {1295124}, mrreviewer = {Stephen Gelbart}, doi = {10.4153/CJM-1994-053-4}, url = {https://doi.org/10.4153/CJM-1994-053-4}, zblnumber = {0829.22031}, }
[HLR] $Go to document$ G. Harder, R. P. Langlands, and M. Rapoport, "Algebraische Zyklen auf Hilbert-Blumenthal-Flächen," J. Reine Angew. Math., vol. 366, pp. 53-120, 1986.

Show bibtex

@ARTICLE{HLR, author = {Harder, G. and Langlands, R. P. and Rapoport, M.}, title = {Algebraische {Z}yklen auf {H}ilbert-{B}lumenthal-{F}lächen}, journal = {J. Reine Angew. Math.}, fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, volume = {366}, year = {1986}, pages = {53--120}, issn = {0075-4102}, mrclass = {11G40 (14C99 14G13 14J20)}, mrnumber = {0833013}, mrreviewer = {Thomas Zink}, zblnumber = {0575.14004}, doi = {10.1515/crll.1986.366.53}, url = {https://doi.org/10.1515/crll.1986.366.53}, }
[HT] M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, Princeton Univ. Press, Princeton, NJ, 2001, vol. 151.

Show bibtex

@BOOK{HT, author = {Harris, Michael and Taylor, Richard}, title = {The Geometry and Cohomology of Some Simple {S}himura Varieties}, series = {Ann. of Math. Stud.}, volume = {151}, note = {with an appendix by Vladimir G. Berkovich}, publisher = {Princeton Univ. Press, Princeton, NJ}, year = {2001}, pages = {viii+276}, isbn = {0-691-09090-4}, mrclass = {11G18 (11F70 11S37 14G35 22E45)}, mrnumber = {1876802}, mrreviewer = {James Milne}, zblnumber = {1036.11027}, }
[He] $Go to document$ H. He, "On the Gan-Gross-Prasad conjecture for $U(p,q)$," Invent. Math., vol. 209, iss. 3, pp. 837-884, 2017.

Show bibtex

@ARTICLE{He, author = {He, Hongyu}, title = {On the {G}an-{G}ross-{P}rasad conjecture for {$U(p,q)$}}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {209}, year = {2017}, number = {3}, pages = {837--884}, issn = {0020-9910}, mrclass = {22E50 (11F70)}, mrnumber = {3681395}, mrreviewer = {Volker J. Heiermann}, doi = {10.1007/s00222-017-0720-x}, url = {https://doi.org/10.1007/s00222-017-0720-x}, zblnumber = {1375.22009}, }
[H15] $Go to document$ V. Heiermann, "A note on standard modules and Vogan $L$-packets," Manuscripta Math., vol. 150, iss. 3-4, pp. 571-583, 2016.

Show bibtex

@ARTICLE{H15, author = {Heiermann, Volker}, title = {A note on standard modules and {V}ogan {$L$}-packets}, journal = {Manuscripta Math.}, fjournal = {Manuscripta Mathematica}, volume = {150}, year = {2016}, number = {3-4}, pages = {571--583}, issn = {0025-2611}, mrclass = {11F70 (11S37 22E50)}, mrnumber = {3514747}, mrreviewer = {Hang Xue}, doi = {10.1007/s00229-016-0824-4}, url = {https://doi.org/10.1007/s00229-016-0824-4}, zblnumber = {1348.11042}, }
[H00] $Go to document$ G. Henniart, "Une preuve simple des conjectures de Langlands pour ${ GL}(n)$ sur un corps $p$-adique," Invent. Math., vol. 139, iss. 2, pp. 439-455, 2000.

Show bibtex

@ARTICLE{H00, author = {Henniart, Guy}, title = {Une preuve simple des conjectures de {L}anglands pour {${\rm GL}(n)$} sur un corps {$p$}-adique}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {139}, year = {2000}, number = {2}, pages = {439--455}, issn = {0020-9910}, mrclass = {11F70 (11R39 11S37 22E50 22E55)}, mrnumber = {1738446}, mrreviewer = {Dihua Jiang}, doi = {10.1007/s002220050012}, url = {https://doi.org/10.1007/s002220050012}, zblnumber = {1048.11092}, }
[H79] $Go to document$ R. Howe, "Wave front sets of representations of Lie groups," in Automorphic Forms, Representation Theory and Arithmetic, Tata Inst. Fundamental Res., Bombay, 1981, vol. 10, pp. 117-140.

Show bibtex

@INCOLLECTION{H79, author = {Howe, Roger}, title = {Wave front sets of representations of {L}ie groups}, booktitle = {Automorphic Forms, Representation Theory and Arithmetic}, venue = {{B}ombay, 1979}, series = {Tata Inst. Fund. Res. Studies in Math.}, volume = {10}, pages = {117--140}, publisher = {Tata Inst. Fundamental Res., Bombay}, year = {1981}, mrclass = {22E30 (22E45 35S05 58G15)}, mrnumber = {0633659}, mrreviewer = {Linda Preiss Rothschild}, zblnumber = {0494.22010}, doi = {10.1007/978-3-662-00734-1_3}, url = {https://doi.org/10.1007/978-3-662-00734-1_3}, }
[H81] $Go to document$ R. Howe, "Automorphic forms of low rank," in Noncommutative Harmonic Analysis and Lie Groups, Springer-Verlag, New York, 1981, vol. 880, pp. 211-248.

Show bibtex

@INCOLLECTION{H81, author = {Howe, Roger}, title = {Automorphic forms of low rank}, booktitle = {Noncommutative Harmonic Analysis and {L}ie Groups}, venue = {{M}arseille, 1980}, series = {Lecture Notes in Math.}, volume = {880}, pages = {211--248}, publisher = {Springer-Verlag, New York}, year = {1981}, mrclass = {10D40 (22E55)}, mrnumber = {0644835}, mrreviewer = {Audrey A. Terras}, zblnumber = {0463.10015}, doi = {10.1007/BFb0090411}, url = {https://doi.org/10.1007/BFb0090411}, }
[IY] $Go to document$ A. Ichino and S. Yamana, "Periods of automorphic forms: the case of $({ U}_{n+1}\times{ U}_n,{ U}_n)$," J. Reine Angew. Math., vol. 746, pp. 1-38, 2019.

Show bibtex

@ARTICLE{IY, author = {Ichino, Atsushi and Yamana, Shunsuke}, title = {Periods of automorphic forms: the case of {$({\rm U}_{n+1}\times{\rm U}_n,{\rm U}_n)$}}, journal = {J. Reine Angew. Math.}, fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, volume = {746}, year = {2019}, pages = {1--38}, issn = {0075-4102}, mrclass = {11F70 (11F67)}, mrnumber = {3895624}, mrreviewer = {Ramin Takloo-Bighash}, doi = {10.1515/crelle-2015-0107}, url = {https://doi.org/10.1515/crelle-2015-0107}, zblnumber = {06999121}, }
[JR11] H. Jacquet and S. Rallis, "On the Gross-Prasad conjecture for unitary groups," in On Certain $L$-Functions, Amer. Math. Soc., Providence, RI, 2011, vol. 13, pp. 205-264.

Show bibtex

@INCOLLECTION{JR11, author = {Jacquet, Hervé and Rallis, Stephen}, title = {On the {G}ross-{P}rasad conjecture for unitary groups}, booktitle = {On Certain {$L$}-Functions}, series = {Clay Math. Proc.}, volume = {13}, pages = {205--264}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2011}, mrclass = {22E55 (11F72)}, mrnumber = {2767518}, mrreviewer = {Christian A. Zorn}, zblnumber = {1222.22018}, }
[J14] $Go to document$ D. Jiang, "Automorphic integral transforms for classical groups I: Endoscopy correspondences," in Automorphic Forms and Related Geometry: Assessing the Legacy of I. I. Piatetski-Shapiro, Amer. Math. Soc., Providence, RI, 2014, vol. 614, pp. 179-242.

Show bibtex

@INCOLLECTION{J14, author = {Jiang, Dihua}, title = {Automorphic integral transforms for classical groups {I}: {E}ndoscopy correspondences}, booktitle = {Automorphic Forms and Related Geometry: Assessing the Legacy of {I}. {I}. {P}iatetski-{S}hapiro}, series = {Contemp. Math.}, volume = {614}, pages = {179--242}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2014}, mrclass = {22E50 (11F70 11F85 22E55)}, mrnumber = {3220929}, mrreviewer = {Zhengyu Mao}, doi = {10.1090/conm/614/12253}, url = {https://doi.org/10.1090/conm/614/12253}, zblnumber = {1315.11037}, }
[J17] D. Jiang, "On tensor product $L$-functions and Langlands functoriality," Bull. Iranian Math. Soc., vol. 43, iss. 4, pp. 169-189, 2017.

Show bibtex

@ARTICLE{J17, author = {Jiang, D.}, title = {On tensor product {$L$}-functions and {L}anglands functoriality}, journal = {Bull. Iranian Math. Soc.}, fjournal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, year = {2017}, number = {4}, pages = {169--189}, issn = {1017-060X}, mrclass = {11F70 (11F85 22E50)}, mrnumber = {3711827}, mrreviewer = {Anton Deitmar}, zblnumber = {1405.22023}, }
[JL-Cogdell] $Go to document$ D. Jiang and B. Liu, "Fourier coefficients for automorphic forms on quasisplit classical groups," in Advances in the Theory of Automorphic Forms and their $L$-Functions, Amer. Math. Soc., Providence, RI, 2016, vol. 664, pp. 187-208.

Show bibtex

@INCOLLECTION{JL-Cogdell, author = {Jiang, Dihua and Liu, Baiying}, title = {Fourier coefficients for automorphic forms on quasisplit classical groups}, booktitle = {Advances in the Theory of Automorphic Forms and their {$L$}-Functions}, series = {Contemp. Math.}, volume = {664}, pages = {187--208}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2016}, mrclass = {11F70 (11F30 22E55)}, mrnumber = {3502983}, mrreviewer = {Chenyan Wu}, doi = {10.1090/conm/664/13062}, url = {https://doi.org/10.1090/conm/664/13062}, zblnumber = {1418.11095}, }
[JLS] $Go to document$ D. Jiang, B. Liu, and G. Savin, "Raising nilpotent orbits in wave-front sets," Represent. Theory, vol. 20, pp. 419-450, 2016.

Show bibtex

@ARTICLE{JLS, author = {Jiang, Dihua and Liu, Baiying and Savin, Gordan}, title = {Raising nilpotent orbits in wave-front sets}, journal = {Represent. Theory}, fjournal = {Representation Theory. An Electronic Journal of the Amer. Math. Soc.}, volume = {20}, year = {2016}, pages = {419--450}, mrclass = {22E50 (11F70 17B08 20G05 22E35 22E55)}, mrnumber = {3564676}, mrreviewer = {William M. McGovern}, doi = {10.1090/ert/490}, url = {https://doi.org/10.1090/ert/490}, zblnumber = {1417.11087}, }
[JLX] $Go to document$ D. Jiang, B. Liu, and B. Xu, "A reciprocal branching problem for automorphic representations and global Vogan packets," J. Reine Angew. Math., 2019.

Show bibtex

@article{JLX, author = {Jiang, Dihua and Liu, Baiying and Xu, Bin}, title = {A reciprocal branching problem for automorphic representations and global {V}ogan packets}, journal={J. Reine Angew. Math.}, year = {2019}, doi={10.1515/crelle-2019-0016}, }
[JLXZ] $Go to document$ D. Jiang, B. Liu, B. Xu, and L. Zhang, "The Jacquet-Langlands correspondence via twisted descent," Int. Math. Res. Not. IMRN, iss. 18, pp. 5455-5492, 2016.

Show bibtex

@ARTICLE{JLXZ, author = {Jiang, Dihua and Liu, Baiying and Xu, Bin and Zhang, Lei}, title = {The {J}acquet-{L}anglands correspondence via twisted descent}, journal = {Int. Math. Res. Not. IMRN}, fjournal = {International Mathematics Research Notices. IMRN}, year = {2016}, number = {18}, pages = {5455--5492}, issn = {1073-7928}, mrclass = {11F66 (11F30 22E50 22E55)}, mrnumber = {3567248}, mrreviewer = {Yuanqing Cai}, doi = {10.1093/imrn/rnv312}, url = {https://doi.org/10.1093/imrn/rnv312}, zblnumber = {1404.11061}, }
[JLZ13] $Go to document$ D. Jiang, B. Liu, and L. Zhang, "Poles of certain residual Eisenstein series of classical groups," Pacific J. Math., vol. 264, iss. 1, pp. 83-123, 2013.

Show bibtex

@ARTICLE{JLZ13, author = {Jiang, Dihua and Liu, Baiying and Zhang, Lei}, title = {Poles of certain residual {E}isenstein series of classical groups}, journal = {Pacific J. Math.}, fjournal = {Pacific Journal of Mathematics}, volume = {264}, year = {2013}, number = {1}, pages = {83--123}, issn = {0030-8730}, mrclass = {11F70 (11F72 22E50 22E55)}, mrnumber = {3079762}, mrreviewer = {Wen-Wei Li}, doi = {10.2140/pjm.2013.264.83}, url = {https://doi.org/10.2140/pjm.2013.264.83}, zblnumber = {1325.11047}, }
[JS03] $Go to document$ D. Jiang and D. Soudry, "The local converse theorem for ${ SO}(2n+1)$ and applications," Ann. of Math. (2), vol. 157, iss. 3, pp. 743-806, 2003.

Show bibtex

@ARTICLE{JS03, author = {Jiang, Dihua and Soudry, David}, title = {The local converse theorem for {${\rm SO}(2n+1)$} and applications}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {157}, year = {2003}, number = {3}, pages = {743--806}, issn = {0003-486X}, mrclass = {11S37 (22E50)}, mrnumber = {1983781}, doi = {10.4007/annals.2003.157.743}, url = {https://doi.org/10.4007/annals.2003.157.743}, zblnumber = {1049.11055}, }
[JSZ] $Go to document$ D. Jiang, B. Sun, and C. Zhu, "Uniqueness of Bessel models: The Archimedean case," Geom. Funct. Anal., vol. 20, iss. 3, pp. 690-709, 2010.

Show bibtex

@ARTICLE{JSZ, author = {Jiang, Dihua and Sun, Binyong and Zhu, Chen-Bo}, title = {Uniqueness of {B}essel models: The {A}rchimedean case}, journal = {Geom. Funct. Anal.}, fjournal = {Geometric and Functional Analysis}, volume = {20}, year = {2010}, number = {3}, pages = {690--709}, issn = {1016-443X}, mrclass = {22E45}, mrnumber = {2720228}, doi = {10.1007/s00039-010-0077-4}, url = {https://doi.org/10.1007/s00039-010-0077-4}, zblnumber = {1200.22008}, }
[JZ14] $Go to document$ D. Jiang and L. Zhang, "A product of tensor product $L$-functions of quasi-split classical groups of Hermitian type," Geom. Funct. Anal., vol. 24, iss. 2, pp. 552-609, 2014.

Show bibtex

@ARTICLE{JZ14, author = {Jiang, Dihua and Zhang, Lei}, title = {A product of tensor product {$L$}-functions of quasi-split classical groups of {H}ermitian type}, journal = {Geom. Funct. Anal.}, fjournal = {Geometric and Functional Analysis}, volume = {24}, year = {2014}, number = {2}, pages = {552--609}, issn = {1016-443X}, mrclass = {11F70 (11F85 22E55)}, mrnumber = {3192035}, mrreviewer = {Wen-Wei Li}, doi = {10.1007/s00039-014-0266-7}, url = {https://doi.org/10.1007/s00039-014-0266-7}, zblnumber = {1298.11046}, }
[JZ-Howe] D. Jiang and L. Zhang, "Automorphic integral transforms for classical groups II: Twisted descents," in Representation Theory, Number Theory, and Invariant Theory, Birkhäuser/Springer, Cham, 2017, vol. 323, pp. 303-335.

Show bibtex

@INCOLLECTION{JZ-Howe, author = {Jiang, Dihua and Zhang, Lei}, title = {Automorphic integral transforms for classical groups {II}: {T}wisted descents}, booktitle = {Representation Theory, Number Theory, and Invariant Theory}, series = {Progr. Math.}, volume = {323}, pages = {303--335}, publisher = {Birkhäuser/Springer, Cham}, year = {2017}, mrclass = {22E50 (11F70 11F85)}, mrnumber = {3753916}, mrreviewer = {Dubravka Ban}, zblnumber = {1425.11110}, }
[JZ-SLD] $Go to document$ D. Jiang and L. Zhang, "Local root numbers and spectrum of the local descents for orthogonal groups: $p$-adic case," Algebra Number Theory, vol. 12, iss. 6, pp. 1489-1535, 2018.

Show bibtex

@ARTICLE{JZ-SLD, author = {Jiang, Dihua and Zhang, Lei}, title = {Local root numbers and spectrum of the local descents for orthogonal groups: {$p$}-adic case}, journal = {Algebra Number Theory}, fjournal = {Algebra \& Number Theory}, volume = {12}, year = {2018}, number = {6}, pages = {1489--1535}, issn = {1937-0652}, mrclass = {11F70 (11S25 20G25 22E50)}, mrnumber = {3864205}, mrreviewer = {Qing Zhang}, doi = {10.2140/ant.2018.12.1489}, url = {https://doi.org/10.2140/ant.2018.12.1489}, zblnumber = {06973918}, }
[JZ-UnU1] $Go to document$ D. Jiang and L. Zhang, "On the non-vanishing of the central value of certain $L$-functions: unitary groups," J. European Math. Soc., 2020.

Show bibtex

@article{JZ-UnU1, author = {Jiang, Dihua and Zhang, Lei}, title = {On the non-vanishing of the central value of certain $L$-functions: unitary groups}, journal={J. European Math. Soc.}, year = {2020}, doi = {10.4171/JEMS/955}, }
[JZ] D. Jiang and L. Zhang, Bessel descents and branching problems, 2019.

Show bibtex

@MISC{JZ, author = {Jiang, Dihua and Zhang, Lei}, title = {Bessel descents and branching problems}, arxiv = {1905.02307v1}, year = {2019}, zblnumber = {}, }
[Klocal] $Go to document$ T. Kaletha, "Rigid inner forms of real and $p$-adic groups," Ann. of Math. (2), vol. 184, iss. 2, pp. 559-632, 2016.

Show bibtex

@ARTICLE{Klocal, author = {Kaletha, Tasho}, title = {Rigid inner forms of real and {$p$}-adic groups}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {184}, year = {2016}, number = {2}, pages = {559--632}, issn = {0003-486X}, mrclass = {20G25 (14L17 20G10)}, mrnumber = {3548533}, mrreviewer = {Wen-Wei Li}, doi = {10.4007/annals.2016.184.2.6}, url = {https://doi.org/10.4007/annals.2016.184.2.6}, zblnumber = {1393.22009}, }
[Kglobal] $Go to document$ T. Kaletha, "Global rigid inner forms and multiplicities of discrete automorphic representations," Invent. Math., vol. 213, iss. 1, pp. 271-369, 2018.

Show bibtex

@ARTICLE{Kglobal, author = {Kaletha, Tasho}, title = {Global rigid inner forms and multiplicities of discrete automorphic representations}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {213}, year = {2018}, number = {1}, pages = {271--369}, issn = {0020-9910}, mrclass = {11R34}, mrnumber = {3815567}, mrreviewer = {Meng Fai Lim}, doi = {10.1007/s00222-018-0791-3}, url = {https://doi.org/10.1007/s00222-018-0791-3}, zblnumber = {1415.11079}, }
[KMSW] T. Kaletha, A. Minguez, S. G. Shin, and P. White, Endoscopic Classification of Representations: Inner Forms of Unitary Groups, 2014.

Show bibtex

@MISC{KMSW, author = {Kaletha, Tasho and Minguez, Alberto and Shin, S. G. and White, Paul-James}, title = {Endoscopic Classification of Representations: {I}nner Forms of Unitary Groups}, arxiv = {1409.3731}, year = {2014}, zblnumber = {}, }
[K87] N. Kawanaka, "Shintani lifting and Gel\cprime fand-Graev representations," in The Arcata Conference on Representations of Finite Groups, Amer. Math. Soc., Providence, RI, 1987, vol. 47, pp. 147-163.

Show bibtex

@INCOLLECTION{K87, author = {Kawanaka, Noriaki}, title = {Shintani lifting and {G}el\cprime fand-{G}raev representations}, booktitle = {The {A}rcata {C}onference on {R}epresentations of {F}inite {G}roups}, venue = {{A}rcata, {C}alif., 1986}, series = {Proc. Sympos. Pure Math.}, volume = {47}, pages = {147--163}, publisher = {Amer. Math. Soc., Providence, RI}, year = {1987}, mrclass = {22E50 (20G05)}, mrnumber = {0933357}, mrreviewer = {Marie-France Vignéras}, zblnumber = {0654.20046}, }
[K05] $Go to document$ H. H. Kim, "On local $L$-functions and normalized intertwining operators," Canad. J. Math., vol. 57, iss. 3, pp. 535-597, 2005.

Show bibtex

@ARTICLE{K05, author = {Kim, Henry H.}, title = {On local {$L$}-functions and normalized intertwining operators}, journal = {Canad. J. Math.}, fjournal = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques}, volume = {57}, year = {2005}, number = {3}, pages = {535--597}, issn = {0008-414X}, mrclass = {11F70 (22E55)}, mrnumber = {2134402}, mrreviewer = {Mahdi Asgari}, doi = {10.4153/CJM-2005-023-x}, url = {https://doi.org/10.4153/CJM-2005-023-x}, zblnumber = {1096.11019}, }
[L71] R. P. Langlands, Euler Products, Yale Univ. Press, New Haven, CT, 1971.

Show bibtex

@BOOK{L71, author = {Langlands, Robert P.}, title = {Euler Products}, note = {A James K. Whittemore Lecture in Mathematics given at Yale Univ., 1967, {\em Yale Math. Monogr.} {\bf 1}}, publisher = {Yale Univ. Press, New Haven, CT}, year = {1971}, pages = {v+53}, mrclass = {10D20 (22E55)}, mrnumber = {0419366}, mrreviewer = {Stephen Gelbart}, zblnumber = {0231.20016}, }
[L76] R. P. Langlands, On the Functional Equations Satisfied by Eisenstein Series, Springer-Verlag, New York, 1976, vol. 544.

Show bibtex

@BOOK{L76, author = {Langlands, Robert P.}, title = {On the Functional Equations Satisfied by {E}isenstein Series}, series = {Lecture Notes in Math.}, volume = {544}, publisher = {Springer-Verlag, New York}, year = {1976}, pages = {v+337}, mrclass = {22E55 (10C15 10D20 32N05)}, mrnumber = {0579181}, mrreviewer = {James G. Arthur}, zblnumber = {0332.10018}, }
[L89] $Go to document$ R. P. Langlands, "On the classification of irreducible representations of real algebraic groups," in Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Amer. Math. Soc., Providence, RI, 1989, vol. 31, pp. 101-170.

Show bibtex

@INCOLLECTION{L89, author = {Langlands, R. P.}, title = {On the classification of irreducible representations of real algebraic groups}, booktitle = {Representation Theory and Harmonic Analysis on Semisimple {L}ie Groups}, series = {Math. Surveys Monogr.}, volume = {31}, pages = {101--170}, publisher = {Amer. Math. Soc., Providence, RI}, year = {1989}, mrclass = {22E45 (22E46)}, mrnumber = {1011897}, mrreviewer = {D. Mili\v{c}ić}, doi = {10.1090/surv/031/03}, url = {https://doi.org/10.1090/surv/031/03}, zblnumber = {0741.22009}, }
[LiuYF14] $Go to document$ Y. Liu, "Relative trace formulae toward Bessel and Fourier-Jacobi periods on unitary groups," Manuscripta Math., vol. 145, iss. 1-2, pp. 1-69, 2014.

Show bibtex

@ARTICLE{LiuYF14, author = {Liu, Yifeng}, title = {Relative trace formulae toward {B}essel and {F}ourier-{J}acobi periods on unitary groups}, journal = {Manuscripta Math.}, fjournal = {Manuscripta Mathematica}, volume = {145}, year = {2014}, number = {1-2}, pages = {1--69}, issn = {0025-2611}, mrclass = {11F67}, mrnumber = {3244725}, mrreviewer = {Alexandru A. Popa}, doi = {10.1007/s00229-014-0666-x}, url = {https://doi.org/10.1007/s00229-014-0666-x}, zblnumber = {1301.11050}, }
[Luo-thesis] Z. Luo, A formula for regular nilpotent germs and the local Gan-Gross-Prasad conjecture for special orthogonal groups: archimedean case, 2021.

Show bibtex

@MISC{Luo-thesis, author = {Luo, Zhilin}, title = {A formula for regular nilpotent germs and the local {G}an-{G}ross-{P}rasad conjecture for special orthogonal groups: archimedean case}, note = {Ph.D. Thesis, Univ. of Minnesota}, year = {2021}, zblnumber = {}, }
[M96] $Go to document$ C. Moeglin, "Front d’onde des représentations des groupes classiques $p$-adiques," Amer. J. Math., vol. 118, iss. 6, pp. 1313-1346, 1996.

Show bibtex

@ARTICLE{M96, author = {M{\oe}glin, C.}, title = {Front d'onde des représentations des groupes classiques {$p$}-adiques}, journal = {Amer. J. Math.}, fjournal = {American Journal of Mathematics}, volume = {118}, year = {1996}, number = {6}, pages = {1313--1346}, issn = {0002-9327}, mrclass = {22E50 (20G25)}, mrnumber = {1420926}, mrreviewer = {David Manderscheid}, doi = {10.1353/ajm.1996.0051}, url = {https://doi.org/10.1353/ajm.1996.0051}, zblnumber = {0864.22007}, }
[M08] $Go to document$ C. Moeglin, "Formes automorphes de carré intégrable non cuspidales," Manuscripta Math., vol. 127, iss. 4, pp. 411-467, 2008.

Show bibtex

@ARTICLE{M08, author = {M{\oe}glin, C.}, title = {Formes automorphes de carré intégrable non cuspidales}, journal = {Manuscripta Math.}, fjournal = {Manuscripta Mathematica}, volume = {127}, year = {2008}, number = {4}, pages = {411--467}, issn = {0025-2611}, mrclass = {11F70 (22E55)}, mrnumber = {2457189}, mrreviewer = {Anne-Marie H. Aubert}, doi = {10.1007/s00229-008-0205-8}, url = {https://doi.org/10.1007/s00229-008-0205-8}, zblnumber = {1306.11041}, }
[M11] $Go to document$ C. Moeglin, "Image des opérateurs d’entrelacements normalisés et pôles des séries d’Eisenstein," Adv. Math., vol. 228, iss. 2, pp. 1068-1134, 2011.

Show bibtex

@ARTICLE{M11, author = {M{\oe}glin, C.}, title = {Image des opérateurs d'entrelacements normalisés et pôles des séries d'{E}isenstein}, journal = {Adv. Math.}, fjournal = {Advances in Mathematics}, volume = {228}, year = {2011}, number = {2}, pages = {1068--1134}, issn = {0001-8708}, mrclass = {22E50 (11F03 11M36)}, mrnumber = {2822218}, mrreviewer = {Anne-Marie H. Aubert}, doi = {10.1016/j.aim.2011.06.003}, url = {https://doi.org/10.1016/j.aim.2011.06.003}, zblnumber = {1225.22016}, }
[M12] $Go to document$ C. Moeglin, "Fonctions $L$ de paires pour les groupes classiques," Ramanujan J., vol. 28, iss. 2, pp. 187-209, 2012.

Show bibtex

@ARTICLE{M12, author = {M{\oe}glin, C.}, title = {Fonctions {$L$} de paires pour les groupes classiques}, journal = {Ramanujan J.}, fjournal = {Ramanujan Journal. An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan}, volume = {28}, year = {2012}, number = {2}, pages = {187--209}, issn = {1382-4090}, mrclass = {11F70 (11F27)}, mrnumber = {2925174}, doi = {10.1007/s11139-012-9372-z}, url = {https://doi.org/10.1007/s11139-012-9372-z}, zblnumber = {1273.11088}, }
[MW87] $Go to document$ C. Moeglin and J. -L. Waldspurger, "Modèles de Whittaker dégénérés pour des groupes $p$-adiques," Math. Z., vol. 196, iss. 3, pp. 427-452, 1987.

Show bibtex

@ARTICLE{MW87, author = {M{\oe}glin, C. and Waldspurger, J.-L.}, title = {Modèles de {W}hittaker dégénérés pour des groupes {$p$}-adiques}, journal = {Math. Z.}, fjournal = {Mathematische Zeitschrift}, volume = {196}, year = {1987}, number = {3}, pages = {427--452}, issn = {0025-5874}, mrclass = {22E50 (11F70 11S37)}, mrnumber = {0913667}, mrreviewer = {Mitsuo Sugiura}, doi = {10.1007/BF01200363}, url = {https://doi.org/10.1007/BF01200363}, zblnumber = {0612.22008}, }
[MW89] $Go to document$ C. Moeglin and J. -L. Waldspurger, "Le spectre résiduel de ${ GL}(n)$," Ann. Sci. École Norm. Sup. (4), vol. 22, iss. 4, pp. 605-674, 1989.

Show bibtex

@ARTICLE{MW89, author = {M{\oe}glin, C. and Waldspurger, J.-L.}, title = {Le spectre résiduel de {${\rm GL}(n)$}}, journal = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, fjournal = {Annales Scientifiques de l'\'{E}cole Normale Supérieure. Quatrième Série}, volume = {22}, year = {1989}, number = {4}, pages = {605--674}, issn = {0012-9593}, mrclass = {22E55 (11F70 22E50)}, mrnumber = {1026752}, mrreviewer = {Stephen Gelbart}, doi = {10.24033/asens.1595}, url = {https://doi.org/10.24033/asens.1595}, zblnumber = {0696.10023}, }
[MW95] $Go to document$ C. Moeglin and J. -L. Waldspurger, Spectral Decomposition and Eisenstein Series, Cambridge Univ. Press, Cambridge, 1995, vol. 113.

Show bibtex

@BOOK{MW95, author = {M{\oe}glin, C. and Waldspurger, J.-L.}, title = {Spectral Decomposition and {E}isenstein Series}, series = {Cambridge Tracts in Math.}, volume = {113}, note = {Une paraphrase de l'\'{E}criture [A paraphrase of Scripture]}, publisher = {Cambridge Univ. Press, Cambridge}, year = {1995}, pages = {xxviii+338}, isbn = {0-521-41893-3}, mrclass = {11F70 (22E55)}, mrnumber = {1361168}, mrreviewer = {Joe Repka}, doi = {10.1017/CBO9780511470905}, url = {https://doi.org/10.1017/CBO9780511470905}, zblnumber = {0846.11032}, }
[MW12] C. Moeglin and J. Waldspurger, "La conjecture locale de Gross-Prasad pour les groupes spéciaux orthogonaux: le cas général," in Sur les conjectures de Gross et Prasad. II, Math. Soc. France, Paris, 2012, vol. 347, pp. 167-216.

Show bibtex

@INCOLLECTION{MW12, author = {M{\oe}glin, C. and Waldspurger, Jean-Loup}, title = {La conjecture locale de {G}ross-{P}rasad pour les groupes spéciaux orthogonaux: le cas général}, booktitle = {Sur les conjectures de Gross et Prasad. II}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {347}, year = {2012}, pages = {167--216}, issn = {0303-1179}, isbn = {978-2-85629-350-8}, mrclass = {22E50}, mrnumber = {3155346}, zblnumber = {1276.22007}, }
[MW-Book1] C. Moeglin and J. Waldspurger, Stabilisation de la Formule des Traces tordue. Vol. 1, Birkhäuser/Springer, Cham, 2016, vol. 316.

Show bibtex

@BOOK{MW-Book1, author = {M{\oe}glin, C. and Waldspurger, Jean-Loup}, title = {Stabilisation de la Formule des Traces tordue. {V}ol. 1}, series = {Progr. in Math.}, volume = {316}, publisher = {Birkhäuser/Springer, Cham}, year = {2016}, pages = {xviii+587}, isbn = {978-3-319-30048-1; 978-3-319-30049-8}, mrclass = {22E50 (11F70 11F72 22E55)}, mrnumber = {3823813}, mrreviewer = {Jean-Pierre Labesse}, zblnumber = {1361.11004}, }
[MW-Book2] C. Moeglin and J. Waldspurger, Stabilisation de la Formule des Traces Tordue. Vol. 2, Birkhäuser/Springer, Cham, 2016, vol. 317.

Show bibtex

@BOOK{MW-Book2, author = {M{\oe}glin, C. and Waldspurger, Jean-Loup}, title = {Stabilisation de la Formule des Traces Tordue. {V}ol. 2}, series = {Progr. Math.}, volume = {317}, publisher = {Birkhäuser/Springer, Cham}, year = {2016}, pages = {v--xxviii and 589--1315}, isbn = {978-3-319-30057-3; 978-3-319-30058-0}, mrclass = {22E50 (11F70 11F72 22E55)}, mrnumber = {3823814}, mrreviewer = {Jean-Pierre Labesse}, zblnumber = {1381.11001}, }
[Mk15] $Go to document$ C. P. Mok, "Endoscopic classification of representations of quasi-split unitary groups," Mem. Amer. Math. Soc., vol. 235, iss. 1108, p. vi, 2015.

Show bibtex

@ARTICLE{Mk15, author = {Mok, Chung Pang}, title = {Endoscopic classification of representations of quasi-split unitary groups}, journal = {Mem. Amer. Math. Soc.}, fjournal = {Memoirs of the Amer. Math. Soc.}, volume = {235}, year = {2015}, number = {1108}, pages = {vi+248}, issn = {0065-9266}, isbn = {978-1-4704-1041-4; 978-1-4704-2226-4}, mrclass = {22E55 (11R42 22E50)}, mrnumber = {3338302}, mrreviewer = {Neven Grbac}, doi = {10.1090/memo/1108}, url = {https://doi.org/10.1090/memo/1108}, zblnumber = {1316.22018}, }
[Sch] $Go to document$ P. Scholze, "The local Langlands correspondence for $\mathrm{GL}_n$ over $p$-adic fields," Invent. Math., vol. 192, iss. 3, pp. 663-715, 2013.

Show bibtex

@ARTICLE{Sch, author = {Scholze, Peter}, title = {The local {L}anglands correspondence for {$\mathrm{GL}_n$} over {$p$}-adic fields}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {192}, year = {2013}, number = {3}, pages = {663--715}, issn = {0020-9910}, mrclass = {22E50 (11G18 14G35)}, mrnumber = {3049932}, mrreviewer = {Maarten Sander Solleveld}, doi = {10.1007/s00222-012-0420-5}, url = {https://doi.org/10.1007/s00222-012-0420-5}, zblnumber = {1305.22025}, }
[Sh10] $Go to document$ F. Shahidi, Eisenstein Series and Automorphic $L$-Functions, Amer. Math. Soc., Providence, RI, 2010, vol. 58.

Show bibtex

@BOOK{Sh10, author = {Shahidi, Freydoon}, title = {Eisenstein Series and Automorphic {$L$}-Functions}, series = {Amer. Math. Soc. Colloq. Publ.}, volume = {58}, publisher = {Amer. Math. Soc., Providence, RI}, year = {2010}, pages = {vi+210}, isbn = {978-0-8218-4989-7}, mrclass = {11F70 (11-02 11M36 11R42 22E50 22E55)}, mrnumber = {2683009}, mrreviewer = {M. Ram Murty}, doi = {10.1090/coll/058}, url = {https://doi.org/10.1090/coll/058}, zblnumber = {1215.11054}, }
[S93] $Go to document$ D. Soudry, "Rankin-Selberg convolutions for ${ SO}_{2l+1}\times{ GL}_n$: local theory," Mem. Amer. Math. Soc., vol. 105, iss. 500, p. vi, 1993.

Show bibtex

@ARTICLE{S93, author = {Soudry, David}, title = {Rankin-{S}elberg convolutions for {${\rm SO}_{2l+1}\times{\rm GL}_n$}: local theory}, journal = {Mem. Amer. Math. Soc.}, fjournal = {Memoirs of the Amer. Math. Soc.}, volume = {105}, year = {1993}, number = {500}, pages = {vi+100}, issn = {0065-9266}, mrclass = {11F70 (11F67 22E50)}, mrnumber = {1169228}, mrreviewer = {David Joyner}, doi = {10.1090/memo/0500}, url = {https://doi.org/10.1090/memo/0500}, zblnumber = {0805.22007}, }
[S-ICM] D. Soudry, "Rankin-Selberg integrals, the descent method, and Langlands functoriality," in International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1311-1325.

Show bibtex

@INCOLLECTION{S-ICM, author = {Soudry, David}, title = {Rankin-{S}elberg integrals, the descent method, and {L}anglands functoriality}, booktitle = {International {C}ongress of {M}athematicians. {V}ol. {II}}, pages = {1311--1325}, publisher = {Eur. Math. Soc., Zürich}, year = {2006}, mrclass = {11F70 (11R39 22E55)}, mrnumber = {2275646}, mrreviewer = {Joseph A. Hundley}, zblnumber = {1130.11024}, }
[JSdZ] D. Jiang, D. Soudry, and L. Zhang, The unramified computation of Rankin-Selberg integrals for quasisplit classical groups: Bessel model case.

Show bibtex

@misc{JSdZ, author = {Jiang, Dihua and Soudry, David and Zhang, Lei}, title={The unramified computation of {R}ankin-{S}elberg integrals for quasisplit classical groups: {B}essel model case}, note={in preparation}, sortyear={2021}, }
[S-I] $Go to document$ D. Soudry, "The unramified computation of Rankin-Selberg integrals expressed in terms of Bessel models for split orthogonal groups: Part I," Israel J. Math., vol. 222, iss. 2, pp. 711-786, 2017.

Show bibtex

@ARTICLE{S-I, author = {Soudry, David}, title = {The unramified computation of {R}ankin-{S}elberg integrals expressed in terms of {B}essel models for split orthogonal groups: {P}art {I}}, journal = {Israel J. Math.}, fjournal = {Israel Journal of Mathematics}, volume = {222}, year = {2017}, number = {2}, pages = {711--786}, issn = {0021-2172}, mrclass = {11F70 (11F66 22E55)}, mrnumber = {3722265}, mrreviewer = {Wen-Wei Li}, doi = {10.1007/s11856-017-1604-x}, url = {https://doi.org/10.1007/s11856-017-1604-x}, zblnumber = {06821078}, }
[S-II] $Go to document$ D. Soudry, "The unramified computation of Rankin-Selberg integrals expressed in terms of Bessel models for split orthogonal groups: Part II," J. Number Theory, vol. 186, pp. 62-102, 2018.

Show bibtex

@ARTICLE{S-II, author = {Soudry, David}, title = {The unramified computation of {R}ankin-{S}elberg integrals expressed in terms of {B}essel models for split orthogonal groups: {P}art {II}}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {186}, year = {2018}, pages = {62--102}, issn = {0022-314X}, mrclass = {11F70 (11F66 22E55)}, mrnumber = {3758206}, mrreviewer = {Ravi Raghunathan}, doi = {10.1016/j.jnt.2017.10.026}, url = {https://doi.org/10.1016/j.jnt.2017.10.026}, zblnumber = {07003382}, }
[SZ] $Go to document$ B. Sun and C. Zhu, "Multiplicity one theorems: the Archimedean case," Ann. of Math. (2), vol. 175, iss. 1, pp. 23-44, 2012.

Show bibtex

@ARTICLE{SZ, author = {Sun, Binyong and Zhu, Chen-Bo}, title = {Multiplicity one theorems: the {A}rchimedean case}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {175}, year = {2012}, number = {1}, pages = {23--44}, issn = {0003-486X}, mrclass = {22E45 (22E30)}, mrnumber = {2874638}, mrreviewer = {Andre Reznikov}, doi = {10.4007/annals.2012.175.1.2}, url = {https://doi.org/10.4007/annals.2012.175.1.2}, zblnumber = {1239.22014}, }
[T86] $Go to document$ M. Tadić, "Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)," Ann. Sci. École Norm. Sup. (4), vol. 19, iss. 3, pp. 335-382, 1986.

Show bibtex

@ARTICLE{T86, author = {Tadi{ć}, Marko}, title = {Classification of unitary representations in irreducible representations of general linear group (non-{A}rchimedean case)}, journal = {Ann. Sci. \'{E}cole Norm. Sup. (4)}, fjournal = {Annales Scientifiques de l'\'{E}cole Normale Supérieure. Quatrième Série}, volume = {19}, year = {1986}, number = {3}, pages = {335--382}, issn = {0012-9593}, mrclass = {22E50}, mrnumber = {0870688}, mrreviewer = {D. Mili\v{c}ić}, doi = {10.24033/asens.1510}, url = {https://doi.org/10.24033/asens.1510}, zblnumber = {0614.22005}, }
[V86] $Go to document$ D. A. Vogan Jr., "The unitary dual of ${ GL}(n)$ over an Archimedean field," Invent. Math., vol. 83, iss. 3, pp. 449-505, 1986.

Show bibtex

@ARTICLE{V86, author = {Vogan, Jr., David A.}, title = {The unitary dual of {${\rm GL}(n)$} over an {A}rchimedean field}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {83}, year = {1986}, number = {3}, pages = {449--505}, issn = {0020-9910}, mrclass = {22E46}, mrnumber = {0827363}, mrreviewer = {D. Mili\v{c}ić}, doi = {10.1007/BF01394418}, url = {https://doi.org/10.1007/BF01394418}, zblnumber = {0598.22008}, }
[V93] $Go to document$ D. A. Vogan Jr., "The local Langlands conjecture," in Representation Theory of Groups and Algebras, Amer. Math. Soc., Providence, RI, 1993, vol. 145, pp. 305-379.

Show bibtex

@INCOLLECTION{V93, author = {Vogan, Jr., David A.}, title = {The local {L}anglands conjecture}, booktitle = {Representation Theory of Groups and Algebras}, series = {Contemp. Math.}, volume = {145}, pages = {305--379}, publisher = {Amer. Math. Soc., Providence, RI}, year = {1993}, mrclass = {22E50 (11S37)}, mrnumber = {1216197}, mrreviewer = {Ernst-Wilhelm Zink}, doi = {10.1090/conm/145/1216197}, url = {https://doi.org/10.1090/conm/145/1216197}, zblnumber = {0802.22005}, }
[W03] $Go to document$ J. -L. Waldspurger, "La formule de Plancherel pour les groupes $p$-adiques (d’après Harish-Chandra)," J. Inst. Math. Jussieu, vol. 2, iss. 2, pp. 235-333, 2003.

Show bibtex

@ARTICLE{W03, author = {Waldspurger, J.-L.}, title = {La formule de {P}lancherel pour les groupes {$p$}-adiques (d'après {H}arish-{C}handra)}, journal = {J. Inst. Math. Jussieu}, fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu}, volume = {2}, year = {2003}, number = {2}, pages = {235--333}, issn = {1474-7480}, mrclass = {22E35 (22E50)}, mrnumber = {1989693}, mrreviewer = {Rebecca Herb}, doi = {10.1017/S1474748003000082}, url = {https://doi.org/10.1017/S1474748003000082}, zblnumber = {1029.22016}, }
[W] J. Waldspurger, "La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux," in Sur les Conjectures de Gross et Prasad. II, Math. Soc. France, Paris, 2012, vol. 347, pp. 103-165.

Show bibtex

@INCOLLECTION{W, author = {Waldspurger, Jean-Loup}, title = {La conjecture locale de {G}ross-{P}rasad pour les représentations tempérées des groupes spéciaux orthogonaux}, booktitle = {Sur les Conjectures de Gross et Prasad. II}, series = {Astérisque}, publisher = {Math. Soc. France, Paris}, volume = {347}, year = {2012}, pages = {103--165}, issn = {0303-1179}, isbn = {978-2-85629-350-8}, mrclass = {22E50}, mrnumber = {3155345}, zblnumber = {1257.22002}, }
[Xu] $Go to document$ B. Xu, Endoscopic Classification of Representations of GSp(2n) and GSO(2n), ProQuest LLC, Ann Arbor, MI, 2014.

Show bibtex

@BOOK{Xu, author = {Xu, Bin}, title = {Endoscopic {C}lassification of {R}epresentations of {GS}p(2n) and {GSO}(2n)}, note = {Thesis (Ph.D.)--Univ. of Toronto (Canada)}, publisher = {ProQuest LLC, Ann Arbor, MI}, year = {2014}, pages = {169}, isbn = {978-1321-67483-5}, mrclass = {Thesis}, mrnumber = {3347095}, url = {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3688703}, zblnumber = {}, }
[XueH14] $Go to document$ H. Xue, "The Gan-Gross-Prasad conjecture for ${ U}(n)\times{ U}(n)$," Adv. Math., vol. 262, pp. 1130-1191, 2014.

Show bibtex

@ARTICLE{XueH14, author = {Xue, Hang}, title = {The {G}an-{G}ross-{P}rasad conjecture for {${\rm U}(n)\times{\rm U}(n)$}}, journal = {Adv. Math.}, fjournal = {Advances in Mathematics}, volume = {262}, year = {2014}, pages = {1130--1191}, issn = {0001-8708}, mrclass = {11F70 (22E55)}, mrnumber = {3228451}, mrreviewer = {Ivan Matić}, doi = {10.1016/j.aim.2014.06.010}, url = {https://doi.org/10.1016/j.aim.2014.06.010}, zblnumber = {1301.11051}, }
[XueH17] $Go to document$ H. Xue, "Refined global Gan-Gross-Prasad conjecture for Fourier-Jacobi periods on symplectic groups," Compos. Math., vol. 153, iss. 1, pp. 68-131, 2017.

Show bibtex

@ARTICLE{XueH17, author = {Xue, Hang}, title = {Refined global {G}an-{G}ross-{P}rasad conjecture for {F}ourier-{J}acobi periods on symplectic groups}, journal = {Compos. Math.}, fjournal = {Compositio Mathematica}, volume = {153}, year = {2017}, number = {1}, pages = {68--131}, issn = {0010-437X}, mrclass = {11F70 (22E55)}, mrnumber = {3622873}, mrreviewer = {Nadya Gurevich}, doi = {10.1112/S0010437X16007752}, url = {https://doi.org/10.1112/S0010437X16007752}, zblnumber = {06782018}, }
[Zh] $Go to document$ L. Zhang, "Whittaker-Shintani functions for general linear groups over $p$-adic fields," Sci. China Math., vol. 61, iss. 1, pp. 95-110, 2018.

Show bibtex

@ARTICLE{Zh, author = {Zhang, Lei}, title = {Whittaker-{S}hintani functions for general linear groups over {$p$}-adic fields}, journal = {Sci. China Math.}, fjournal = {Science China. Mathematics}, volume = {61}, year = {2018}, number = {1}, pages = {95--110}, issn = {1674-7283}, mrclass = {22E50 (11F70 11F85 22E35)}, mrnumber = {3744401}, mrreviewer = {Ivan Matić}, doi = {10.1007/s11425-016-9064-6}, url = {https://doi.org/10.1007/s11425-016-9064-6}, zblnumber = {1406.22021}, }
[ZW-1] $Go to document$ W. Zhang, "Fourier transform and the global Gan-Gross-Prasad conjecture for unitary groups," Ann. of Math. (2), vol. 180, iss. 3, pp. 971-1049, 2014.

Show bibtex

@ARTICLE{ZW-1, author = {Zhang, Wei}, title = {Fourier transform and the global {G}an-{G}ross-{P}rasad conjecture for unitary groups}, journal = {Ann. of Math. (2)}, fjournal = {Annals of Mathematics. Second Series}, volume = {180}, year = {2014}, number = {3}, pages = {971--1049}, issn = {0003-486X}, mrclass = {11F70 (11F67)}, mrnumber = {3245011}, mrreviewer = {Shuichiro Takeda}, doi = {10.4007/annals.2014.180.3.4}, url = {https://doi.org/10.4007/annals.2014.180.3.4}, zblnumber = {1322.11048}, }
[ZW-2] $Go to document$ W. Zhang, "Automorphic period and the central value of Rankin-Selberg L-function," J. Amer. Math. Soc., vol. 27, iss. 2, pp. 541-612, 2014.

Show bibtex

@ARTICLE{ZW-2, author = {Zhang, Wei}, title = {Automorphic period and the central value of {R}ankin-{S}elberg {L}-function}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the Amer. Math. Soc.}, volume = {27}, year = {2014}, number = {2}, pages = {541--612}, issn = {0894-0347}, mrclass = {11F67 (11F70 11G40 22E55)}, mrnumber = {3164988}, mrreviewer = {Neven Grbac}, doi = {10.1090/S0894-0347-2014-00784-0}, url = {https://doi.org/10.1090/S0894-0347-2014-00784-0}, zblnumber = {1294.11069}, }

Arthur parameters and cuspidal automorphic modules of classical groups

Abstract

Authors