Types for tame $p$-adic groups

Jessica Fintzen

doi:https://doi.org/10.4007/annals.2021.193.1.4

Abstract

Let $k$ be a non-archimedean local field with residual characteristic $p$. Let $G$ be a connected reductive group over $k$ that splits over a tamely ramified field extension of $k$. Suppose $p$ does not divide the order of the Weyl group of $G$. Then we show that every smooth irreducible complex representation of $G(k)$ contains an $\mathfrak {s}$-type of the form constructed by Kim–Yu and that every irreducible supercuspidal representation arises from Yu’s construction. This improves an earlier result of Kim, which held only in characteristic zero and with a very large and ineffective bound on $p$. By contrast, our bound on $p$ is explicit and tight, and our result holds in positive characteristic as well. Moreover, our approach is more explicit in extracting an input for Yu’s construction from a given representation.

Show/hide bibliography for this article

[Adler] $Go to document$ J. D. Adler, "Refined anisotropic $K$-types and supercuspidal representations," Pacific J. Math., vol. 185, iss. 1, pp. 1-32, 1998.

Show bibtex

@ARTICLE{Adler, author = {Adler, Jeffrey D.}, title = {Refined anisotropic {$K$}-types and supercuspidal representations}, journal = {Pacific J. Math.}, fjournal = {Pacific Journal of Mathematics}, volume = {185}, year = {1998}, number = {1}, pages = {1--32}, issn = {0030-8730}, mrclass = {22E50 (22E35)}, mrnumber = {1653184}, mrreviewer = {David Goldberg}, doi = {10.2140/pjm.1998.185.1}, url = {https://doi.org/10.2140/pjm.1998.185.1}, zblnumber = {0924.22015}, }
[Adler-DeBacker] $Go to document$ J. D. Adler and S. DeBacker, "Some applications of Bruhat-Tits theory to harmonic analysis on the Lie algebra of a reductive $p$-adic group," Michigan Math. J., vol. 50, iss. 2, pp. 263-286, 2002.

Show bibtex

@ARTICLE{Adler-DeBacker, author = {Adler, Jeffrey D. and DeBacker, Stephen}, title = {Some applications of {B}ruhat-{T}its theory to harmonic analysis on the {L}ie algebra of a reductive {$p$}-adic group}, journal = {Michigan Math. J.}, fjournal = {Michigan Mathematical Journal}, volume = {50}, year = {2002}, number = {2}, pages = {263--286}, issn = {0026-2285}, mrclass = {22E50 (43A99)}, mrnumber = {1914065}, mrreviewer = {David A. Renard}, doi = {10.1307/mmj/1028575734}, url = {https://doi.org/10.1307/mmj/1028575734}, zblnumber = {1018.22013}, }
[Adler-Roche] $Go to document$ J. D. Adler and A. Roche, "An intertwining result for $p$-adic groups," Canad. J. Math., vol. 52, iss. 3, pp. 449-467, 2000.

Show bibtex

@ARTICLE{Adler-Roche, author = {Adler, Jeffrey D. and Roche, Alan}, title = {An intertwining result for {$p$}-adic groups}, journal = {Canad. J. Math.}, fjournal = {Canadian Journal of Mathematics. Journal Canadien de Mathématiques}, volume = {52}, year = {2000}, number = {3}, pages = {449--467}, issn = {0008-414X}, mrclass = {22E50 (20G25)}, mrnumber = {1758228}, mrreviewer = {Roberto Johnson}, doi = {10.4153/CJM-2000-021-8}, url = {https://doi.org/10.4153/CJM-2000-021-8}, zblnumber = {1160.22304}, }
[Bernstein] J. N. Bernstein, "Le “centre” de Bernstein," in Representations of Reductive Groups over a Local Field, Hermann, Paris, 1984, pp. 1-32.

Show bibtex

@INCOLLECTION{Bernstein, author = {Bernstein, J. N.}, title = {Le ``centre'' de {B}ernstein}, booktitle = {Representations of Reductive Groups over a Local Field}, series = {Travaux en Cours}, pages = {1--32}, note = {Edited by P. Deligne}, publisher = {Hermann, Paris}, year = {1984}, mrclass = {22E50}, mrnumber = {0771671}, mrreviewer = {François Rodier}, zblnumber = {0599.22016}, }
[Borel] $Go to document$ A. Borel, Linear Algebraic Groups, Second ed., Springer-Verlag, New York, 1991, vol. 126.

Show bibtex

@BOOK{Borel, author = {Borel, Armand}, title = {Linear Algebraic Groups}, series = {Graduate Texts in Math.}, volume = {126}, edition = {Second}, publisher = {Springer-Verlag, New York}, year = {1991}, pages = {xii+288}, isbn = {0-387-97370-2}, mrclass = {20-01 (20Gxx)}, mrnumber = {1102012}, mrreviewer = {F. D. Veldkamp}, doi = {10.1007/978-1-4612-0941-6}, url = {https://doi.org/10.1007/978-1-4612-0941-6}, zblnumber = {0726.20030}, }
[Borel-Tits-unipotent] $Go to document$ A. Borel and J. Tits, "Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I," Invent. Math., vol. 12, iss. 2, pp. 95-104, 1971.

Show bibtex

@ARTICLE{Borel-Tits-unipotent, author = {Borel, Armand and Tits, J.}, title = {\'{E}léments unipotents et sous-groupes paraboliques de groupes réductifs. {I}}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {12}, number={2}, year = {1971}, pages = {95--104}, issn = {0020-9910}, mrclass = {20G15}, mrnumber = {0294349}, mrreviewer = {E. J. Taft}, doi = {10.1007/BF01404653}, url = {https://doi.org/10.1007/BF01404653}, zblnumber = {0238.20055}, }
[Bourbaki-4-6] N. Bourbaki, Lie Groups and Lie Algebras. Chapters 4–6, Springer-Verlag, Berlin, 2002.

Show bibtex

@BOOK{Bourbaki-4-6, author = {Bourbaki, Nicolas}, title = {Lie Groups and {L}ie Algebras. {C}hapters 4--6}, series = {Elements of Math. (Berlin)}, note = {translated from the 1968 French original by Andrew Pressley}, publisher = {Springer-Verlag, Berlin}, year = {2002}, pages = {xii+300}, isbn = {3-540-42650-7}, mrclass = {17-01 (00A05 20E42 20F55 22-01)}, mrnumber = {1890629}, zblnumber = {0983.17001}, }
[Broussous] $Go to document$ P. Broussous, "Extension du formalisme de Bushnell et Kutzko au cas d’une algèbre à division," Proc. London Math. Soc. (3), vol. 77, iss. 2, pp. 292-326, 1998.

Show bibtex

@ARTICLE{Broussous, author = {Broussous, P.}, title = {Extension du formalisme de {B}ushnell et {K}utzko au cas d'une algèbre à division}, journal = {Proc. London Math. Soc. (3)}, fjournal = {Proceedings of the London Mathematical Society. Third Series}, volume = {77}, year = {1998}, number = {2}, pages = {292--326}, issn = {0024-6115}, mrclass = {22E50 (11S37)}, mrnumber = {1635145}, mrreviewer = {Ernst-Wilhelm Zink}, doi = {10.1112/s0024611598000471}, url = {https://doi.org/10.1112/s0024611598000471}, zblnumber = {0912.22007}, }
[BK] $Go to document$ C. J. Bushnell and P. C. Kutzko, The Admissible Dual of ${ GL}(N)$ via Compact Open Subgroups, Princeton Univ. Press, Princeton, NJ, 1993, vol. 129.

Show bibtex

@BOOK{BK, author = {Bushnell, Colin J. and Kutzko, Philip C.}, title = {The Admissible Dual of {${\rm GL}(N)$} via Compact Open Subgroups}, series = {Annals of Math. Stud.}, volume = {129}, publisher = {Princeton Univ. Press, Princeton, NJ}, year = {1993}, pages = {xii+313}, isbn = {0-691-03256-4; 0-691-02114-7}, mrclass = {22E50 (22-02)}, mrnumber = {1204652}, mrreviewer = {Mark Reeder}, doi = {10.1515/9781400882496}, url = {https://doi.org/10.1515/9781400882496}, zblnumber = {0787.22016}, }
[BK-SLn] $Go to document$ C. J. Bushnell and P. C. Kutzko, "The admissible dual of ${ SL}(N)$. II," Proc. London Math. Soc. (3), vol. 68, iss. 2, pp. 317-379, 1994.

Show bibtex

@ARTICLE{BK-SLn, author = {Bushnell, Colin J. and Kutzko, Philip C.}, title = {The admissible dual of {${\rm SL}(N)$}. {II}}, journal = {Proc. London Math. Soc. (3)}, fjournal = {Proceedings of the London Mathematical Society. Third Series}, volume = {68}, year = {1994}, number = {2}, pages = {317--379}, issn = {0024-6115}, mrclass = {22E50 (22E35)}, mrnumber = {1253507}, mrreviewer = {Leticia Barchini}, doi = {10.1112/plms/s3-68.2.317}, url = {https://doi.org/10.1112/plms/s3-68.2.317}, zblnumber = {0801.22011}, }
[BK-types] $Go to document$ C. J. Bushnell and P. C. Kutzko, "Smooth representations of reductive $p$-adic groups: structure theory via types," Proc. London Math. Soc. (3), vol. 77, iss. 3, pp. 582-634, 1998.

Show bibtex

@ARTICLE{BK-types, author = {Bushnell, Colin J. and Kutzko, Philip C.}, title = {Smooth representations of reductive {$p$}-adic groups: structure theory via types}, journal = {Proc. London Math. Soc. (3)}, fjournal = {Proceedings of the London Mathematical Society. Third Series}, volume = {77}, year = {1998}, number = {3}, pages = {582--634}, issn = {0024-6115}, mrclass = {22E50 (22E35)}, mrnumber = {1643417}, mrreviewer = {David Goldberg}, doi = {10.1112/S0024611598000574}, url = {https://doi.org/10.1112/S0024611598000574}, zblnumber = {0911.22014}, }
[BK-types-exhaustion] $Go to document$ C. J. Bushnell and P. C. Kutzko, "Semisimple types in ${ GL}_n$," Compositio Math., vol. 119, iss. 1, pp. 53-97, 1999.

Show bibtex

@ARTICLE{BK-types-exhaustion, author = {Bushnell, Colin J. and Kutzko, Philip C.}, title = {Semisimple types in {${\rm GL}_n$}}, journal = {Compositio Math.}, fjournal = {Compositio Mathematica}, volume = {119}, year = {1999}, number = {1}, pages = {53--97}, issn = {0010-437X}, mrclass = {20G05 (20C08 22E50)}, mrnumber = {1711578}, mrreviewer = {Hartmut Schlosser}, doi = {10.1023/A:1001773929735}, url = {https://doi.org/10.1023/A:1001773929735}, zblnumber = {0933.22027}, }
[Carayol] H. Carayol, "Représentations supercuspidales de ${ GL}_{n}$," C. R. Acad. Sci. Paris Sér. A-B, vol. 288, iss. 1, p. a17-a20, 1979.

Show bibtex

@ARTICLE{Carayol, author = {Carayol, Henri}, title = {Représentations supercuspidales de {${\rm GL}\sb{n}$}}, journal = {C. R. Acad. Sci. Paris Sér. A-B}, fjournal = {Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Séries A et B}, volume = {288}, year = {1979}, number = {1}, pages = {A17--A20}, issn = {0151-0509}, mrclass = {22E50}, mrnumber = {0522009}, zblnumber = {0398.22024}, }
[ConradSGA3] B. Conrad, "Reductive group schemes," in Autour des schémas en groupes. Vol. I, Soc. Math. France, Paris, 2014, vol. 42/43, pp. 93-444.

Show bibtex

@INCOLLECTION{ConradSGA3, author = {Conrad, Brian}, title = {Reductive group schemes}, booktitle = {Autour des schémas en groupes. {V}ol. {I}}, series = {Panor. Synthèses}, volume = {42/43}, pages = {93--444}, publisher = {Soc. Math. France, Paris}, year = {2014}, mrclass = {14L15}, mrnumber = {3362641}, zblnumber = {1349.14151}, }
[Pseudoreductive2] $Go to document$ B. Conrad, O. Gabber, and G. Prasad, Pseudo-Reductive Groups, Second ed., Cambridge Univ. Press, Cambridge, 2015, vol. 26.

Show bibtex

@BOOK{Pseudoreductive2, author = {Conrad, Brian and Gabber, Ofer and Prasad, Gopal}, title = {Pseudo-Reductive Groups}, series = {New Math. Monogr.}, volume = {26}, edition = {Second}, publisher = {Cambridge Univ. Press, Cambridge}, year = {2015}, pages = {xxiv+665}, isbn = {978-1-107-08723-1}, mrclass = {20G15 (14L15)}, mrnumber = {3362817}, doi = {10.1017/CBO9781316092439}, url = {https://doi.org/10.1017/CBO9781316092439}, zblnumber = {1314.20037}, }
[Fi] J. Fintzen, On the Moy–Prasad filtration, 2015.

Show bibtex

@MISC{Fi, author = {Fintzen, Jessica}, title = {On the {M}oy--{P}rasad filtration}, note = {{T}o appear in the \emph{Journal of the European Mathematical Society (JEMS)}}, arxiv = {1511.00726}, year = {2015}, zblnumber = {}, }
[Fi-tame-tori] $Go to document$ J. Fintzen, "Tame tori in $p$-adic groups and good semisimple elements," Internat. Math. Res. Not., p. 22, 2019.

Show bibtex

@ARTICLE{Fi-tame-tori, author = {Fintzen, Jessica}, title = {{T}ame tori in $p$-adic groups and good semisimple elements}, journal = {Internat. Math. Res. Not.}, doi ={10.1093/imrn/rnz234}, url = {https://doi.org/10.1093/imrn/rnz234}, year={2019}, pages={22 pp.}, zblnumber = {1253.11041}, }
[FR] $Go to document$ J. Fintzen and B. Romano, "Stable vectors in Moy-Prasad filtrations," Compos. Math., vol. 153, iss. 2, pp. 358-372, 2017.

Show bibtex

@ARTICLE{FR, author = {Fintzen, Jessica and Romano, Beth}, title = {Stable vectors in {M}oy-{P}rasad filtrations}, journal = {Compos. Math.}, fjournal = {Compositio Mathematica}, volume = {153}, year = {2017}, number = {2}, pages = {358--372}, issn = {0010-437X}, mrclass = {22E50 (11S37 14L24 20G25)}, mrnumber = {3705228}, mrreviewer = {U. K. Anandavardhanan}, doi = {10.1112/S0010437X16008228}, url = {https://doi.org/10.1112/S0010437X16008228}, zblnumber = {1373.22024}, }
[Gerardin] $Go to document$ P. Gérardin, "Weil representations associated to finite fields," J. Algebra, vol. 46, iss. 1, pp. 54-101, 1977.

Show bibtex

@ARTICLE{Gerardin, author = {G{é}rardin, Paul}, title = {Weil representations associated to finite fields}, journal = {J. Algebra}, fjournal = {Journal of Algebra}, volume = {46}, year = {1977}, number = {1}, pages = {54--101}, issn = {0021-8693}, mrclass = {20G05}, mrnumber = {0460477}, mrreviewer = {G. I. Lehrer}, doi = {10.1016/0021-8693(77)90394-5}, url = {https://doi.org/10.1016/0021-8693(77)90394-5}, zblnumber = {0359.20008}, }
[Goldberg-Roche] $Go to document$ D. Goldberg and A. Roche, "Types in ${ SL}_n$," Proc. London Math. Soc. (3), vol. 85, iss. 1, pp. 119-138, 2002.

Show bibtex

@ARTICLE{Goldberg-Roche, author = {Goldberg, David and Roche, Alan}, title = {Types in {${\rm SL}_n$}}, journal = {Proc. London Math. Soc. (3)}, fjournal = {Proceedings of the London Mathematical Society. Third Series}, volume = {85}, year = {2002}, number = {1}, pages = {119--138}, issn = {0024-6115}, mrclass = {22E50}, mrnumber = {1901371}, mrreviewer = {Shu-Yen Pan}, doi = {10.1112/S002461150201359X}, url = {https://doi.org/10.1112/S002461150201359X}, zblnumber = {1011.22008}, }
[Hakim-Murnaghan] $Go to document$ J. Hakim and F. Murnaghan, "Distinguished tame supercuspidal representations," Int. Math. Res. Pap. IMRP, iss. 2, p. 166, 2008.

Show bibtex

@ARTICLE{Hakim-Murnaghan, author = {Hakim, Jeffrey and Murnaghan, Fiona}, title = {Distinguished tame supercuspidal representations}, journal = {Int. Math. Res. Pap. IMRP}, fjournal = {International Mathematics Research Papers. IMRP}, year = {2008}, number = {2}, note = {Art. ID rpn005}, pages = {166 pp.}, issn = {1687-3017}, mrclass = {22E50}, mrnumber = {2431732}, mrreviewer = {Shaun A. R. Stevens}, doi = {10.1093/imrp/rpn005}, url = {https://doi.org/10.1093/imrp/rpn005}, zblnumber = {1160.22008}, }
[Howe] $Go to document$ R. E. Howe, "Tamely ramified supercuspidal representations of ${ Gl}_{n}$," Pacific J. Math., vol. 73, iss. 2, pp. 437-460, 1977.

Show bibtex

@ARTICLE{Howe, author = {Howe, Roger E.}, title = {Tamely ramified supercuspidal representations of {${\rm Gl}\sb{n}$}}, journal = {Pacific J. Math.}, fjournal = {Pacific Journal of Mathematics}, volume = {73}, year = {1977}, number = {2}, pages = {437--460}, issn = {0030-8730}, mrclass = {22E50}, mrnumber = {0492087}, mrreviewer = {Allan J. Silberger}, doi = {10.2140/pjm.1977.73.437}, url = {https://doi.org/10.2140/pjm.1977.73.437}, zblnumber = {0404.22019}, }
[Kaletha] $Go to document$ T. Kaletha, "Regular supercuspidal representations," J. Amer. Math. Soc., vol. 32, iss. 4, pp. 1071-1170, 2019.

Show bibtex

@ARTICLE{Kaletha, author = {Kaletha, Tasho}, title = {Regular supercuspidal representations}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {32}, year = {2019}, number = {4}, pages = {1071--1170}, issn = {0894-0347}, mrclass = {22E50 (11F70 11S37)}, mrnumber = {4013740}, doi = {10.1090/jams/925}, url = {https://doi.org/10.1090/jams/925}, zblnumber = {07121118}, }
[Kempf] $Go to document$ G. R. Kempf, "Instability in invariant theory," Ann. of Math. (2), vol. 108, iss. 2, pp. 299-316, 1978.

Show bibtex

@ARTICLE{Kempf, author = {Kempf, G. R.}, title = {Instability in invariant theory}, journal = {Ann. of Math. (2)}, volume = {108}, number = {2}, year = {1978}, pages = {299--316}, mrnumber = {506989}, doi = {10.2307/1971168}, url = {http://dx.doi.org.proxy.lib.umich.edu/10.2307/1971168}, zblnumber = {0406.14031}, }
[Kim] $Go to document$ J. Kim, "Supercuspidal representations: an exhaustion theorem," J. Amer. Math. Soc., vol. 20, iss. 2, pp. 273-320, 2007.

Show bibtex

@ARTICLE{Kim, author = {Kim, Ju-Lee}, title = {Supercuspidal representations: an exhaustion theorem}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {20}, year = {2007}, number = {2}, pages = {273--320}, issn = {0894-0347}, mrclass = {22E50 (20G25 22E35)}, mrnumber = {2276772}, mrreviewer = {U. K. Anandavardhanan}, doi = {10.1090/S0894-0347-06-00544-3}, url = {https://doi.org/10.1090/S0894-0347-06-00544-3}, zblnumber = {1111.22015}, }
[Kim-Murnaghan] $Go to document$ J. Kim and F. Murnaghan, "Character expansions and unrefined minimal $K$-types," Amer. J. Math., vol. 125, iss. 6, pp. 1199-1234, 2003.

Show bibtex

@ARTICLE{Kim-Murnaghan, author = {Kim, Ju-Lee and Murnaghan, Fiona}, title = {Character expansions and unrefined minimal {$K$}-types}, journal = {Amer. J. Math.}, fjournal = {American Journal of Mathematics}, volume = {125}, year = {2003}, number = {6}, pages = {1199--1234}, issn = {0002-9327}, mrclass = {22E50 (17B45 20G25)}, mrnumber = {2018660}, mrreviewer = {Ernst-Wilhelm Zink}, doi = {10.1353/ajm.2003.0043}, url = {https://doi.org/10.1353/ajm.2003.0043}, zblnumber = {1037.22035}, }
[KimYu] $Go to document$ J. Kim and J. Yu, "Construction of tame types," in Representation Theory, Number Theory, and Invariant Theory, Birkhäuser/Springer, Cham, 2017, vol. 323, pp. 337-357.

Show bibtex

@INCOLLECTION{KimYu, author = {Kim, Ju-Lee and Yu, Jiu-Kang}, title = {Construction of tame types}, booktitle = {Representation Theory, Number Theory, and Invariant Theory}, series = {Progr. Math.}, volume = {323}, pages = {337--357}, publisher = {Birkhäuser/Springer, Cham}, year = {2017}, mrclass = {22E50}, mrnumber = {3753917}, mrreviewer = {Alan Roche}, doi = {10.1007/978-3-319-59728-7_12}, url = {https://doi.org/10.1007/978-3-319-59728-7_12}, zblnumber = {1409.22012}, }
[Miyauchi-Stevens] $Go to document$ M. Miyauchi and S. Stevens, "Semisimple types for $p$-adic classical groups," Math. Ann., vol. 358, iss. 1-2, pp. 257-288, 2014.

Show bibtex

@ARTICLE{Miyauchi-Stevens, author = {Miyauchi, Michitaka and Stevens, Shaun}, title = {Semisimple types for {$p$}-adic classical groups}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {358}, year = {2014}, number = {1-2}, pages = {257--288}, issn = {0025-5831}, mrclass = {22E50}, mrnumber = {3157998}, mrreviewer = {Cristina Maria Ballantine}, doi = {10.1007/s00208-013-0953-y}, url = {https://doi.org/10.1007/s00208-013-0953-y}, zblnumber = {1294.22015}, }
[Morris] $Go to document$ L. Morris, "Tamely ramified intertwining algebras," Invent. Math., vol. 114, iss. 1, pp. 1-54, 1993.

Show bibtex

@ARTICLE{Morris, author = {Morris, Lawrence}, title = {Tamely ramified intertwining algebras}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {114}, year = {1993}, number = {1}, pages = {1--54}, issn = {0020-9910}, mrclass = {22E50 (20G25)}, mrnumber = {1235019}, mrreviewer = {Mark Reeder}, doi = {10.1007/BF01232662}, url = {https://doi.org/10.1007/BF01232662}, zblnumber = {0854.22022}, }
[Morris-depth-zero] $Go to document$ L. Morris, "Level zero $\bf G$-types," Compositio Math., vol. 118, iss. 2, pp. 135-157, 1999.

Show bibtex

@ARTICLE{Morris-depth-zero, author = {Morris, Lawrence}, title = {Level zero {$\bf G$}-types}, journal = {Compositio Math.}, fjournal = {Compositio Mathematica}, volume = {118}, year = {1999}, number = {2}, pages = {135--157}, issn = {0010-437X}, mrclass = {22E50}, mrnumber = {1713308}, mrreviewer = {Goran Muić}, doi = {10.1023/A:1001019027614}, url = {https://doi.org/10.1023/A:1001019027614}, zblnumber = {0937.22011}, }
[Moy-exhaustion] $Go to document$ A. Moy, "Local constants and the tame Langlands correspondence," Amer. J. Math., vol. 108, iss. 4, pp. 863-930, 1986.

Show bibtex

@ARTICLE{Moy-exhaustion, author = {Moy, A.}, title = {Local constants and the tame {L}anglands correspondence}, journal = {Amer. J. Math.}, volume = {108}, number = {4}, year = {1986}, pages = {863--930}, mrnumber = {853218}, doi = {10.2307/2374518}, zblnumber = {0597.12019}, }
[MP1] $Go to document$ A. Moy and G. Prasad, "Unrefined minimal $K$-types for $p$-adic groups," Invent. Math., vol. 116, iss. 1-3, pp. 393-408, 1994.

Show bibtex

@ARTICLE{MP1, author = {Moy, Allen and Prasad, Gopal}, title = {Unrefined minimal {$K$}-types for {$p$}-adic groups}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {116}, year = {1994}, number = {1-3}, pages = {393--408}, issn = {0020-9910}, mrclass = {22E50 (20G05)}, mrnumber = {1253198}, mrreviewer = {David Goldberg}, doi = {10.1007/BF01231566}, url = {https://doi.org/10.1007/BF01231566}, zblnumber = {0804.22008}, }
[MP2] $Go to document$ A. Moy and G. Prasad, "Jacquet functors and unrefined minimal $K$-types," Comment. Math. Helv., vol. 71, iss. 1, pp. 98-121, 1996.

Show bibtex

@ARTICLE{MP2, author = {Moy, Allen and Prasad, Gopal}, title = {Jacquet functors and unrefined minimal {$K$}-types}, journal = {Comment. Math. Helv.}, fjournal = {Commentarii Mathematici Helvetici}, volume = {71}, year = {1996}, number = {1}, pages = {98--121}, issn = {0010-2571}, mrclass = {22E50 (22E35)}, mrnumber = {1371680}, mrreviewer = {Mark Reeder}, doi = {10.5169/seals-53837}, url = {https://doi.org/10.5169/seals-53837}, zblnumber = {0860.22006}, }
[ReederYu] $Go to document$ M. Reeder and J. Yu, "Epipelagic representations and invariant theory," J. Amer. Math. Soc., vol. 27, iss. 2, pp. 437-477, 2014.

Show bibtex

@ARTICLE{ReederYu, author = {Reeder, Mark and Yu, Jiu-Kang}, title = {Epipelagic representations and invariant theory}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {27}, year = {2014}, number = {2}, pages = {437--477}, issn = {0894-0347}, mrclass = {22E50 (11S15)}, mrnumber = {3164986}, mrreviewer = {Marko Tadić}, doi = {10.1090/S0894-0347-2013-00780-8}, url = {https://doi.org/10.1090/S0894-0347-2013-00780-8}, zblnumber = {1284.22011}, }
[Secherre-Stevens] $Go to document$ V. Sécherre and S. Stevens, "Représentations lisses de ${ GL}_m(D)$. IV. Représentations supercuspidales," J. Inst. Math. Jussieu, vol. 7, iss. 3, pp. 527-574, 2008.

Show bibtex

@ARTICLE{Secherre-Stevens, author = {Sécherre, V. and Stevens, S.}, title = {Représentations lisses de {${\rm GL}_m(D)$}. {IV}. {R}eprésentations supercuspidales}, journal = {J. Inst. Math. Jussieu}, fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu}, volume = {7}, year = {2008}, number = {3}, pages = {527--574}, issn = {1474-7480}, mrclass = {22E50}, mrnumber = {2427423}, doi = {10.1017/S1474748008000078}, url = {https://doi.org/10.1017/S1474748008000078}, zblnumber = {1140.22014}, }
[Secherre-Stevens-types] $Go to document$ V. Sécherre and S. Stevens, "Smooth representations of $GL_m(D)$ VI: semisimple types," Int. Math. Res. Not. IMRN, iss. 13, pp. 2994-3039, 2012.

Show bibtex

@ARTICLE{Secherre-Stevens-types, author = {Sécherre, Vincent and Stevens, Shaun}, title = {Smooth representations of {$GL_m(D)$} {VI}: semisimple types}, journal = {Int. Math. Res. Not. IMRN}, fjournal = {International Mathematics Research Notices. IMRN}, year = {2012}, number = {13}, pages = {2994--3039}, issn = {1073-7928}, mrclass = {22E50}, mrnumber = {2946230}, mrreviewer = {C. Ryan Vinroot}, doi = {10.1093/imrn/rnr122}, url = {https://doi.org/10.1093/imrn/rnr122}, zblnumber = {1246.22023}, }
[Springer-Steinberg] $Go to document$ T. A. Springer and R. Steinberg, "Conjugacy classes," in Seminar on Algebraic Groups and Related Finite Groups, Springer-Verlag, Berlin, 1970, vol. 131, pp. 167-266.

Show bibtex

@INCOLLECTION{Springer-Steinberg, author = {Springer, T. A. and Steinberg, R.}, title = {Conjugacy classes}, booktitle = {Seminar on {A}lgebraic {G}roups and {R}elated {F}inite {G}roups}, venue = {{T}he {I}nstitute for {A}dvanced {S}tudy, {P}rinceton, {N}.{J}., 1968/69)}, series = {Lecture Notes in Math.}, volume = {131}, pages = {167--266}, publisher = {Springer-Verlag, Berlin}, year = {1970}, mrclass = {14.50 (20.00)}, mrnumber = {0268192}, mrreviewer = {N. Burgoyne}, doi = {10.1007/BFb0081546}, url = {https://doi.org/10.1007/BFb0081546}, zblnumber = {0249.20024}, }
[Steinberg-torsion] $Go to document$ R. Steinberg, "Torsion in reductive groups," Advances in Math., vol. 15, pp. 63-92, 1975.

Show bibtex

@ARTICLE{Steinberg-torsion, author = {Steinberg, Robert}, title = {Torsion in reductive groups}, journal = {Advances in Math.}, fjournal = {Advances in Mathematics}, volume = {15}, year = {1975}, pages = {63--92}, issn = {0001-8708}, mrclass = {20G15}, mrnumber = {0354892}, mrreviewer = {S. I. Gel\cprime fand}, doi = {10.1016/0001-8708(75)90125-5}, url = {https://doi.org/10.1016/0001-8708(75)90125-5}, zblnumber = {0312.20026}, }
[Stevens] $Go to document$ S. Stevens, "The supercuspidal representations of $p$-adic classical groups," Invent. Math., vol. 172, iss. 2, pp. 289-352, 2008.

Show bibtex

@ARTICLE{Stevens, author = {Stevens, Shaun}, title = {The supercuspidal representations of {$p$}-adic classical groups}, journal = {Invent. Math.}, fjournal = {Inventiones Mathematicae}, volume = {172}, year = {2008}, number = {2}, pages = {289--352}, issn = {0020-9910}, mrclass = {22E50}, mrnumber = {2390287}, mrreviewer = {Anne-Marie H. Aubert}, doi = {10.1007/s00222-007-0099-1}, url = {https://doi.org/10.1007/s00222-007-0099-1}, zblnumber = {1140.22016}, }
[Yu] $Go to document$ J. Yu, "Construction of tame supercuspidal representations," J. Amer. Math. Soc., vol. 14, iss. 3, pp. 579-622, 2001.

Show bibtex

@ARTICLE{Yu, author = {Yu, Jiu-Kang}, title = {Construction of tame supercuspidal representations}, journal = {J. Amer. Math. Soc.}, fjournal = {Journal of the American Mathematical Society}, volume = {14}, year = {2001}, number = {3}, pages = {579--622}, issn = {0894-0347}, mrclass = {22E50}, mrnumber = {1824988}, mrreviewer = {Bertrand Lemaire}, doi = {10.1090/S0894-0347-01-00363-0}, url = {https://doi.org/10.1090/S0894-0347-01-00363-0}, zblnumber = {0971.22012}, }
[Zink] $Go to document$ E. -W. Zink, "Representation theory of local division algebras," J. Reine Angew. Math., vol. 428, pp. 1-44, 1992.

Show bibtex

@ARTICLE{Zink, author = {Zink, E.-W.}, title = {Representation theory of local division algebras}, journal = {J. Reine Angew. Math.}, volume = {428}, year = {1992}, pages = {1--44}, mrnumber = {1166506}, doi = {10.1515/crll.1992.428.1}, url = {https://doi.org/10.1515/crll.1992.428.1}, zblnumber = {0745.22018}, }

Types for tame $p$-adic groups

Abstract

Authors