Abstract
We prove the rank 1 case of a conjecture of Frenkel-Gaitsgory: critical level Kac-Moody representations with regular central characters localize onto the affine Grassmannian. The method uses an analogue in local geometric Langlands of the existence of Whittaker models for most representations of $\mathrm {GL}_2$ over a non-Archimedean field.
-
[arakawa-fiebig]
T. Arakawa and P. Fiebig, "On the restricted Verma modules at the critical level," Trans. Amer. Math. Soc., vol. 364, iss. 9, pp. 4683-4712, 2012.
@ARTICLE{arakawa-fiebig,
author = {Arakawa, Tomoyuki and Fiebig, Peter},
title = {On the restricted {V}erma modules at the critical level},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the Amer. Math. Soc.},
volume = {364},
year = {2012},
number = {9},
pages = {4683--4712},
issn = {0002-9947},
mrclass = {17B67 (17B10 81R10)},
mrnumber = {2922606},
mrreviewer = {Stefano Capparelli},
doi = {10.1090/S0002-9947-2012-05467-5},
url = {https://doi.org/10.1090/S0002-9947-2012-05467-5},
zblnumber = {1352.17025},
} -
[dima-opers] D. Arinkin, Irreducible connections admit generic oper structures, 2016.
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author = {Arinkin, D.},
title = {Irreducible connections admit generic oper structures},
arxiv = {1602.08989},
year = {2016},
zblnumber = {},
} -
[arinkin-gaitsgory]
D. Arinkin and D. Gaitsgory, "Singular support of coherent sheaves and the geometric Langlands conjecture," Selecta Math. (N.S.), vol. 21, iss. 1, pp. 1-199, 2015.
@ARTICLE{arinkin-gaitsgory,
author = {Arinkin, D. and Gaitsgory, D.},
title = {Singular support of coherent sheaves and the geometric {L}anglands conjecture},
journal = {Selecta Math. (N.S.)},
fjournal = {Selecta Mathematica. New Series},
volume = {21},
year = {2015},
number = {1},
pages = {1--199},
issn = {1022-1824},
mrclass = {14D24 (14A20 14F05 22E57)},
mrnumber = {3300415},
mrreviewer = {Richard P. Thomas},
doi = {10.1007/s00029-014-0167-5},
url = {https://doi.org/10.1007/s00029-014-0167-5},
zblnumber = {1423.14085},
} -
[abbgm]
S. Arkhipov, A. Braverman, R. Bezrukavnikov, D. Gaitsgory, and I. Mirković, "Modules over the small quantum group and semi-infinite flag manifold," Transform. Groups, vol. 10, iss. 3-4, pp. 279-362, 2005.
@ARTICLE{abbgm,
author = {Arkhipov, S. and Braverman, A. and Bezrukavnikov, R. and Gaitsgory, D. and Mirković,
I.},
title = {Modules over the small quantum group and semi-infinite flag manifold},
journal = {Transform. Groups},
fjournal = {Transformation Groups},
volume = {10},
year = {2005},
number = {3-4},
pages = {279--362},
issn = {1083-4362},
mrclass = {14F05 (14M15 17B37)},
mrnumber = {2183116},
doi = {10.1007/s00031-005-0401-5},
url = {https://doi.org/10.1007/s00031-005-0401-5},
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} -
[cdo]
S. Arkhipov and D. Gaitsgory, "Differential operators on the loop group via chiral algebras," Int. Math. Res. Not., iss. 4, pp. 165-210, 2002.
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author = {Arkhipov, S. and Gaitsgory, D.},
title = {Differential operators on the loop group via chiral algebras},
journal = {Int. Math. Res. Not.},
fjournal = {International Mathematics Research Notices},
year = {2002},
number = {4},
pages = {165--210},
issn = {1073-7928},
mrclass = {20G15 (17B67 17B69 22E67)},
mrnumber = {1876958},
mrreviewer = {Igor Yu. Potemine},
doi = {10.1155/S1073792802102078},
url = {https://doi.org/10.1155/S1073792802102078},
zblnumber = {0997.17016},
} -
[arkhipov-bezrukavnikov]
S. Arkhipov and R. Bezrukavnikov, "Perverse sheaves on affine flags and Langlands dual group," Israel J. Math., vol. 170, pp. 135-183, 2009.
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author = {Arkhipov, Sergey and Bezrukavnikov, Roman},
title = {Perverse sheaves on affine flags and {L}anglands dual group},
note = {With an appendix by Bezrukavnikov and Ivan Mirković},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {170},
year = {2009},
pages = {135--183},
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mrclass = {14F05 (14D24 14M15)},
mrnumber = {2506322},
doi = {10.1007/s11856-009-0024-y},
url = {https://doi.org/10.1007/s11856-009-0024-y},
zblnumber = {1214.14011},
} -
[arkhipov-bezrukavnikov-ginzburg]
S. Arkhipov, R. Bezrukavnikov, and V. Ginzburg, "Quantum groups, the loop Grassmannian, and the Springer resolution," J. Amer. Math. Soc., vol. 17, iss. 3, pp. 595-678, 2004.
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author = {Arkhipov, Sergey and Bezrukavnikov, Roman and Ginzburg, Victor},
title = {Quantum groups, the loop {G}rassmannian, and the {S}pringer resolution},
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mrnumber = {2053952},
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doi = {10.1090/S0894-0347-04-00454-0},
url = {https://doi.org/10.1090/S0894-0347-04-00454-0},
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} -
[arkhipov-gaitsgory]
S. Arkhipov and D. Gaitsgory, "Another realization of the category of modules over the small quantum group," Adv. Math., vol. 173, iss. 1, pp. 114-143, 2003.
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author = {Arkhipov, Sergey and Gaitsgory, Dennis},
title = {Another realization of the category of modules over the small quantum group},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {173},
year = {2003},
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mrreviewer = {H. H. Andersen},
doi = {10.1016/S0001-8708(02)00016-6},
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} -
[barlev-notes] J. Barlev, Opers, 2010.
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author = {Barlev, J.},
title = {Opers},
year = {2010},
note = {Lecture notes; available on Dennis Gaitsgory's website},
zblnumber = {},
} -
[beilinson-heisenberg]
A. Beilinson, "Langlands parameters for Heisenberg modules," in Studies in Lie theory, Birkhäuser Boston, Boston, MA, 2006, vol. 243, pp. 51-60.
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author = {Beilinson, A.},
title = {Langlands parameters for {H}eisenberg modules},
booktitle = {Studies in {L}ie theory},
series = {Progr. Math.},
volume = {243},
pages = {51--60},
publisher = {Birkhäuser Boston, Boston, MA},
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mrnumber = {2214245},
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doi = {10.1007/0-8176-4478-4\_4},
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} -
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year = {1981},
number = {1},
pages = {15--18},
issn = {0249-6291},
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zblnumber = {0476.14019},
} -
[hitchin] S. Beilinson and V. Drinfeld, Quantization of Hitchin’s integrable system and Hecke eigensheaves.
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author = {Beilinson, Sasha and Drinfeld, Vladimir},
title = {Quantization of {H}itchin's integrable system and {H}ecke eigensheaves},
note={available on authors' websites},
zblnumber = {},
} -
[chiral]
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author = {Beilinson, Alexander and Drinfeld, Vladimir},
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series = {Amer. Math. Soc. Colloq. Publ.},
volume = {51},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2004},
pages = {vi+375},
isbn = {0-8218-3528-9},
mrclass = {17Bxx (14F43)},
mrnumber = {2058353},
mrreviewer = {Francisco J. Plaza Mart\'ın},
doi = {10.1090/coll/051},
url = {https://doi.org/10.1090/coll/051},
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} -
[bzgo]
D. Ben-Zvi, S. Gunningham, and H. Orem, "Highest weights for categorical representations," Int. Math. Res. Not. IMRN, iss. 24, pp. 9988-10004, 2020.
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author = {Ben-Zvi, David and Gunningham, Sam and Orem, Hendrik},
title = {Highest weights for categorical representations},
journal = {Int. Math. Res. Not. IMRN},
fjournal = {International Mathematics Research Notices. IMRN},
year = {2020},
number = {24},
pages = {9988--10004},
issn = {1073-7928},
mrclass = {18M05 (20G05)},
mrnumber = {4190394},
doi = {10.1093/imrn/rny258},
url = {https://doi.org/10.1093/imrn/rny258},
zblnumber = {07323437},
} -
@BOOK{beraldo-*/!,
author = {Beraldo, Dario},
title = {Loop Group Actions on Categories and {W}hittaker Invariants},
note = {Ph.D. Thesis, Univ. of California, Berkeley},
year = {2013},
pages = {86},
isbn = {978-1303-83193-5},
mrclass = {Thesis},
mrnumber = {3232225},
url = {https://escholarship.org/uc/item/0fg9019s},
zblnumber = {},
} -
[bezrukavnikov-hecke]
R. Bezrukavnikov, "On two geometric realizations of an affine Hecke algebra," Publ. Math. Inst. Hautes Études Sci., vol. 123, pp. 1-67, 2016.
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author = {Bezrukavnikov, Roman},
title = {On two geometric realizations of an affine {H}ecke algebra},
journal = {Publ. Math. Inst. Hautes \'{E}tudes Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes \'{E}tudes Scientifiques},
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issn = {0073-8301},
mrclass = {14D24 (20C08)},
mrnumber = {3502096},
mrreviewer = {Igor V. Nikolaev},
doi = {10.1007/s10240-015-0077-x},
url = {https://doi.org/10.1007/s10240-015-0077-x},
zblnumber = {1345.14017},
} -
[bbm]
R. Bezrukavnikov, A. Braverman, and I. Mirkovic, "Some results about geometric Whittaker model," Adv. Math., vol. 186, iss. 1, pp. 143-152, 2004.
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author = {Bezrukavnikov, Roman and Braverman, Alexander and Mirkovic, Ivan},
title = {Some results about geometric {W}hittaker model},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {186},
year = {2004},
number = {1},
pages = {143--152},
issn = {0001-8708},
mrclass = {20G05},
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mrreviewer = {Valentina A. Kiritchenko},
doi = {10.1016/j.aim.2003.07.011},
url = {https://doi.org/10.1016/j.aim.2003.07.011},
zblnumber = {1071.20039},
} -
[bezrukavnikov-lin]
R. Bezrukavnikov and Q. Lin, "Highest weight modules at the critical level and noncommutative Springer resolution," in Algebraic groups and quantum groups, Amer. Math. Soc., Providence, RI, 2012, vol. 565, pp. 15-27.
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author = {Bezrukavnikov, Roman and Lin, Qian},
title = {Highest weight modules at the critical level and noncommutative {S}pringer resolution},
booktitle = {Algebraic groups and quantum groups},
series = {Contemp. Math.},
volume = {565},
pages = {15--27},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2012},
mrclass = {17B67 (14D24 17B10 22E57)},
mrnumber = {2932419},
mrreviewer = {Rongmin Lu},
doi = {10.1090/conm/565/11188},
url = {https://doi.org/10.1090/conm/565/11188},
zblnumber = {1351.17026},
} -
[bezrukavnikov-mirkovic]
R. Bezrukavnikov and I. Mirković, "Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution," Ann. of Math. (2), vol. 178, iss. 3, pp. 835-919, 2013.
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author = {Bezrukavnikov, Roman and Mirković,
Ivan},
title = {Representations of semisimple {L}ie algebras in prime characteristic and the noncommutative {S}pringer resolution},
note = {With an appendix by Eric Sommers},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {178},
year = {2013},
number = {3},
pages = {835--919},
issn = {0003-486X},
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mrnumber = {3092472},
mrreviewer = {Serge M. Skryabin},
doi = {10.4007/annals.2013.178.3.2},
url = {https://doi.org/10.4007/annals.2013.178.3.2},
zblnumber = {1293.17021},
} -
[finiteness]
V. Drinfeld and D. Gaitsgory, "On some finiteness questions for algebraic stacks," Geom. Funct. Anal., vol. 23, iss. 1, pp. 149-294, 2013.
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author = {Drinfeld, Vladimir and Gaitsgory, Dennis},
title = {On some finiteness questions for algebraic stacks},
journal = {Geom. Funct. Anal.},
fjournal = {Geometric and Functional Analysis},
volume = {23},
year = {2013},
number = {1},
pages = {149--294},
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mrclass = {14A20 (14F05 14F10 18Dxx)},
mrnumber = {3037900},
mrreviewer = {Pawel Sosna},
doi = {10.1007/s00039-012-0204-5},
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} -
[frenkel-eisenbud]
M. Mustactua, "Jet schemes of locally complete intersection canonical singularities," Invent. Math., vol. 145, iss. 3, pp. 397-424, 2001.
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author = {Musta\c{t}\u{a},
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title = {Jet schemes of locally complete intersection canonical singularities},
note = {With an appendix by David Eisenbud and Edward Frenkel},
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number = {3},
pages = {397--424},
issn = {0020-9910},
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mrnumber = {1856396},
mrreviewer = {Eugenii Shustin},
doi = {10.1007/s002220100152},
url = {https://doi.org/10.1007/s002220100152},
zblnumber = {1091.14004},
} -
[ff-critical]
B. Feigin and E. Frenkel, "Affine Kac-Moody algebras at the critical level and Gel$’$fand-Dikiĭ algebras," in Infinite Analysis, Part A, B (Kyoto, 1991), World Sci. Publ., River Edge, NJ, 1992, vol. 16, pp. 197-215.
@INCOLLECTION{ff-critical,
author = {Feigin, Boris and Frenkel, Edward},
title = {Affine {K}ac-{M}oody algebras at the critical level and {G}el{$'$}fand-{D}ikiĭ algebras},
booktitle = {Infinite {A}nalysis, {P}art {A},
{B} ({K}yoto, 1991)},
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} -
[frenkel-wakimoto]
E. Frenkel, "Wakimoto modules, opers and the center at the critical level," Adv. Math., vol. 195, iss. 2, pp. 297-404, 2005.
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author = {Frenkel, Edward},
title = {Wakimoto modules, opers and the center at the critical level},
journal = {Adv. Math.},
fjournal = {Advances in Mathematics},
volume = {195},
year = {2005},
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url = {https://doi.org/10.1016/j.aim.2004.08.002},
zblnumber = {1129.17014},
} -
[fg1]
E. Frenkel and D. Gaitsgory, "$D$-modules on the affine Grassmannian and representations of affine Kac-Moody algebras," Duke Math. J., vol. 125, iss. 2, pp. 279-327, 2004.
@ARTICLE{fg1,
author = {Frenkel, Edward and Gaitsgory, Dennis},
title = {{$D$}-modules on the affine {G}rassmannian and representations of affine {K}ac-{M}oody algebras},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {125},
year = {2004},
number = {2},
pages = {279--327},
issn = {0012-7094},
mrclass = {17B67},
mrnumber = {2096675},
mrreviewer = {Stefano Capparelli},
doi = {10.1215/S0012-7094-04-12524-2},
url = {https://doi.org/10.1215/S0012-7094-04-12524-2},
zblnumber = {1107.17013},
} -
[fg2]
E. Frenkel and D. Gaitsgory, "Local geometric Langlands correspondence and affine Kac-Moody algebras," in Algebraic geometry and number theory, Birkhäuser Boston, Boston, MA, 2006, vol. 253, pp. 69-260.
@INCOLLECTION{fg2,
author = {Frenkel, Edward and Gaitsgory, Dennis},
title = {Local geometric {L}anglands correspondence and affine {K}ac-{M}oody algebras},
booktitle = {Algebraic geometry and number theory},
series = {Progr. Math.},
volume = {253},
pages = {69--260},
publisher = {Birkhäuser Boston, Boston, MA},
year = {2006},
mrclass = {17B67 (11G45 11R39 14D20)},
mrnumber = {2263193},
mrreviewer = {Peter Fiebig},
doi = {10.1007/978-0-8176-4532-8\_3},
url = {https://doi.org/10.1007/978-0-8176-4532-8_3},
zblnumber = {1184.17011},
} -
[fg-wakimoto]
E. Frenkel and D. Gaitsgory, "Geometric realizations of Wakimoto modules at the critical level," Duke Math. J., vol. 143, iss. 1, pp. 117-203, 2008.
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author = {Frenkel, Edward and Gaitsgory, Dennis},
title = {Geometric realizations of {W}akimoto modules at the critical level},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {143},
year = {2008},
number = {1},
pages = {117--203},
issn = {0012-7094},
mrclass = {17B67 (14D20)},
mrnumber = {2414746},
mrreviewer = {Stephen Slebarski},
doi = {10.1215/00127094-2008-017},
url = {https://doi.org/10.1215/00127094-2008-017},
zblnumber = {1215.17016},
} -
[dmod-aff-flag]
E. Frenkel and D. Gaitsgory, "$D$-modules on the affine flag variety and representations of affine Kac-Moody algebras," Represent. Theory, vol. 13, pp. 470-608, 2009.
@ARTICLE{dmod-aff-flag,
author = {Frenkel, Edward and Gaitsgory, Dennis},
title = {{$D$}-modules on the affine flag variety and representations of affine {K}ac-{M}oody algebras},
journal = {Represent. Theory},
fjournal = {Representation Theory. An Electronic Journal of the Amer. Math. Soc.},
volume = {13},
year = {2009},
pages = {470--608},
mrclass = {17B67 (13N10 14F05 14F10 17B10)},
mrnumber = {2558786},
mrreviewer = {Guy Rousseau},
doi = {10.1090/S1088-4165-09-00360-4},
url = {https://doi.org/10.1090/S1088-4165-09-00360-4},
zblnumber = {1251.17012},
} -
[fg-spherical]
E. Frenkel and D. Gaitsgory, "Local geometric Langlands correspondence: the spherical case," in Algebraic Analysis and Around, Math. Soc. Japan, Tokyo, 2009, vol. 54, pp. 167-186.
@INCOLLECTION{fg-spherical,
author = {Frenkel, Edward and Gaitsgory, Dennis},
title = {Local geometric {L}anglands correspondence: the spherical case},
booktitle = {Algebraic Analysis and Around},
series = {Adv. Stud. Pure Math.},
volume = {54},
pages = {167--186},
publisher = {Math. Soc. Japan, Tokyo},
year = {2009},
mrclass = {22E57},
mrnumber = {2499556},
mrreviewer = {Peter Fiebig},
doi = {10.2969/aspm/05410167},
url = {https://doi.org/10.2969/aspm/05410167},
zblnumber = {1192.17012},
} -
[fg-loc]
E. Frenkel and D. Gaitsgory, "Localization of $\mathfrak{g}$-modules on the affine Grassmannian," Ann. of Math. (2), vol. 170, iss. 3, pp. 1339-1381, 2009.
@ARTICLE{fg-loc,
author = {Frenkel, Edward and Gaitsgory, Dennis},
title = {Localization of {$\mathfrak{g}$}-modules on the affine {G}rassmannian},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {170},
year = {2009},
number = {3},
pages = {1339--1381},
issn = {0003-486X},
mrclass = {17B67 (14F10 17B10)},
mrnumber = {2600875},
mrreviewer = {Arvid Siqveland},
doi = {10.4007/annals.2009.170.1339},
url = {https://doi.org/10.4007/annals.2009.170.1339},
zblnumber = {1202.17009},
} -
[fgv]
E. Frenkel, D. Gaitsgory, and K. Vilonen, "Whittaker patterns in the geometry of moduli spaces of bundles on curves," Ann. of Math. (2), vol. 153, iss. 3, pp. 699-748, 2001.
@ARTICLE{fgv,
author = {Frenkel, E. and Gaitsgory, D. and Vilonen, K.},
title = {Whittaker patterns in the geometry of moduli spaces of bundles on curves},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {153},
year = {2001},
number = {3},
pages = {699--748},
issn = {0003-486X},
mrclass = {11R39 (11F70 11G45 14D20 22E50)},
mrnumber = {1836286},
mrreviewer = {Igor Yu. Potemine},
doi = {10.2307/2661366},
url = {https://doi.org/10.2307/2661366},
zblnumber = {1070.11050},
} -
[frenkel-teleman]
E. Frenkel and C. Teleman, "Self-extensions of Verma modules and differential forms on opers," Compos. Math., vol. 142, iss. 2, pp. 477-500, 2006.
@ARTICLE{frenkel-teleman,
author = {Frenkel, Edward and Teleman, Constantin},
title = {Self-extensions of {V}erma modules and differential forms on opers},
journal = {Compos. Math.},
fjournal = {Compositio Mathematica},
volume = {142},
year = {2006},
number = {2},
pages = {477--500},
issn = {0010-437X},
mrclass = {17B67 (17B10)},
mrnumber = {2218907},
mrreviewer = {Stefano Capparelli},
doi = {10.1112/S0010437X05001958},
url = {https://doi.org/10.1112/S0010437X05001958},
zblnumber = {1162.17314},
} -
[frenkel-zhu]
E. Frenkel and X. Zhu, "Any flat bundle on a punctured disc has an oper structure," Math. Res. Lett., vol. 17, iss. 1, pp. 27-37, 2010.
@ARTICLE{frenkel-zhu,
author = {Frenkel, Edward and Zhu, Xinwen},
title = {Any flat bundle on a punctured disc has an oper structure},
journal = {Math. Res. Lett.},
fjournal = {Mathematical Research Letters},
volume = {17},
year = {2010},
number = {1},
pages = {27--37},
issn = {1073-2780},
mrclass = {14D24 (17B67 22E67)},
mrnumber = {2592725},
mrreviewer = {Matthias Wendt},
doi = {10.4310/MRL.2010.v17.n1.a3},
url = {https://doi.org/10.4310/MRL.2010.v17.n1.a3},
zblnumber = {1220.14013},
} -
[central]
D. Gaitsgory, "Construction of central elements in the affine Hecke algebra via nearby cycles," Invent. Math., vol. 144, iss. 2, pp. 253-280, 2001.
@ARTICLE{central,
author = {Gaitsgory, D.},
title = {Construction of central elements in the affine {H}ecke algebra via nearby cycles},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {144},
year = {2001},
number = {2},
pages = {253--280},
issn = {0020-9910},
mrclass = {14L15 (14C25 14F05 14M15)},
mrnumber = {1826370},
mrreviewer = {Burt Totaro},
doi = {10.1007/s002220100122},
url = {https://doi.org/10.1007/s002220100122},
zblnumber = {1072.14055},
} -
[twisted-satake]
D. Gaitsgory and S. Lysenko, "Parameters and duality for the metaplectic geometric Langlands theory," Selecta Math. (N.S.), vol. 24, iss. 1, pp. 227-301, 2018.
@ARTICLE{twisted-satake,
author = {Gaitsgory, Dennis and Lysenko, S.},
title = {Parameters and duality for the metaplectic geometric {L}anglands theory},
journal = {Selecta Math. (N.S.)},
fjournal = {Selecta Mathematica. New Series},
volume = {24},
year = {2018},
number = {1},
pages = {227--301},
issn = {1022-1824},
mrclass = {14F05 (14D24 14H60)},
mrnumber = {3769731},
mrreviewer = {Andrew Salch},
doi = {10.1007/s00029-017-0360-4},
url = {https://doi.org/10.1007/s00029-017-0360-4},
zblnumber = {1423.14124},
} -
[quantum-langlands-summary] D. Gaitsgory, Quantum Langlands correspondence, 2007.
@MISC{quantum-langlands-summary, title = {Quantum {L}anglands correspondence},
author = {Gaitsgory, Dennis},
arxiv = {1601.05279},
year = {2007},
zblnumber = {},
} -
[lesjours] D. Gaitsgory, Whittaker categories, 2008.
@MISC{lesjours,
author = {Gaitsgory, Dennis},
title = {Whittaker categories},
note = {formerly titled \emph{Les jours et les travaux},
available on author's website},
year = {2008},
zblnumber = {},
} -
[dgcat] D. Gaitsgory, Generalities on DG categories, 2012.
@MISC{dgcat,
author = {Gaitsgory, Dennis},
title = {Generalities on {DG} categories},
note = {available on author's website},
year = {2012},
zblnumber = {},
} -
@MISC{km-indcoh, title = {Kac-{M}oody representations ({D}ay {IV, T}alk 3)},
author = {Gaitsgory, Dennis},
year = {2014},
url = {https://sites.google.com/site/geometriclanglands2014/notes},
zblnumber = {},
} -
[shvcat]
D. Gaitsgory, "Sheaves of categories and the notion of 1-affineness," in Stacks and Categories in Geometry, Topology, and Algebra, Amer. Math. Soc., Providence, RI, 2015, vol. 643, pp. 127-225.
@INCOLLECTION{shvcat,
author = {Gaitsgory, Dennis},
title = {Sheaves of categories and the notion of 1-affineness},
booktitle = {Stacks and Categories in Geometry, Topology, and Algebra},
series = {Contemp. Math.},
volume = {643},
pages = {127--225},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2015},
mrclass = {14F05 (14A20)},
mrnumber = {3381473},
mrreviewer = {Jon Eivind Vatne},
doi = {10.1090/conm/643/12899},
url = {https://doi.org/10.1090/conm/643/12899},
zblnumber = {1346.14004},
} -
[whit-comp]
D. Gaitsgory, "The local and global versions of the Whittaker category," Pure Appl. Math. Q., vol. 16, iss. 3, pp. 775-904, 2020.
@ARTICLE{whit-comp,
author = {Gaitsgory, Dennis},
title = {The local and global versions of the {W}hittaker category},
journal = {Pure Appl. Math. Q.},
fjournal = {Pure and Applied Mathematics Quarterly},
volume = {16},
year = {2020},
number = {3},
pages = {775--904},
issn = {1558-8599},
mrclass = {14D24 (18D99 18F20 20G25)},
mrnumber = {4176538},
doi = {10.4310/PAMQ.2020.v16.n3.a14},
url = {https://doi.org/10.4310/PAMQ.2020.v16.n3.a14},
zblnumber = {1460.14033},
} -
[crystals]
D. Gaitsgory and N. Rozenblyum, "Crystals and D-modules," Pure Appl. Math. Q., vol. 10, iss. 1, pp. 57-154, 2014.
@ARTICLE{crystals,
author = {Gaitsgory, Dennis and Rozenblyum, Nick},
title = {Crystals and {D}-modules},
journal = {Pure Appl. Math. Q.},
fjournal = {Pure and Applied Mathematics Quarterly},
volume = {10},
year = {2014},
number = {1},
pages = {57--154},
issn = {1558-8599},
mrclass = {14A20 (14F05 14F10)},
mrnumber = {3264953},
mrreviewer = {Andrei D. Halanay},
doi = {10.4310/PAMQ.2014.v10.n1.a2},
url = {https://doi.org/10.4310/PAMQ.2014.v10.n1.a2},
zblnumber = {1327.14013},
} -
[indschemes]
D. Gaitsgory and N. Rozenblyum, "DG indschemes," in Perspectives in representation theory, Amer. Math. Soc., Providence, RI, 2014, vol. 610, pp. 139-251.
@INCOLLECTION{indschemes,
author = {Gaitsgory, Dennis and Rozenblyum, Nick},
title = {D{G} indschemes},
booktitle = {Perspectives in representation theory},
series = {Contemp. Math.},
volume = {610},
pages = {139--251},
publisher = {Amer. Math. Soc., Providence, RI},
year = {2014},
mrclass = {14F05 (18F20)},
mrnumber = {3220628},
mrreviewer = {Jon Eivind Vatne},
doi = {10.1090/conm/610/12080},
url = {https://doi.org/10.1090/conm/610/12080},
zblnumber = {1316.14006},
} -
[grbook]
D. Gaitsgory and N. Rozenblyum, A Study in Derived Algebraic Geometry. Vol. I. Correspondences and Duality, Amer. Math. Soc., Providence, RI, 2017, vol. 221.
@BOOK{grbook,
author = {Gaitsgory, Dennis and Rozenblyum, Nick},
TITLE = {A Study in Derived Algebraic Geometry. {V}ol. {I}. {C}orrespondences and Duality},
SERIES = {Math. Surv. Monogr.},
VOLUME = {221},
PUBLISHER = {Amer. Math. Soc., Providence, RI},
YEAR = {2017},
PAGES = {xl+533pp},
ISBN = {978-1-4704-3569-1},
MRCLASS = {14F05 (18D05 18G55)},
MRNUMBER = {3701352},
MRREVIEWER = {Adrian Langer},
DOI = {10.1090/surv/221.1},
URL = {https://doi.org/10.1090/surv/221.1},
ZBLNUMBER = {1408.14001},
} -
[MR3701353]
D. Gaitsgory and N. Rozenblyum, A Study in Derived Algebraic Geometry. Vol. II. Deformations, Lie Theory and Formal Geometry, Amer. Math. Soc., Providence, RI, 2017, vol. 221.
@book {MR3701353,
author = {Gaitsgory, Dennis and Rozenblyum, Nick},
TITLE = {A Study in Derived Algebraic Geometry. {V}ol. {II}. {D}eformations, {L}ie Theory and Formal Geometry},
SERIES = {Math. Surv. Monogr.},
VOLUME = {221},
PUBLISHER = {Amer. Math. Soc., Providence, RI},
YEAR = {2017},
PAGES = {xxxv+436},
ISBN = {978-1-4704-3570-7},
MRCLASS = {14F05 (18D05 18G55)},
MRNUMBER = {3701353},
MRREVIEWER = {Adrian Langer},
DOI = {10.1090/surv/221.2},
URL = {https://doi.org/10.1090/surv/221.2},
ZBLNUMBER = {1409.14003},
} -
[ginzburg-whittaker-hecke] V. Ginzburg, "Nil-Hecke algebras and Whittaker $\mathcal D$-modules," in Lie Groups, Geometry, and Representation Theory, Birkhäuser/Springer, Cham, 2018, vol. 326, pp. 137-184.
@INCOLLECTION{ginzburg-whittaker-hecke,
author = {Ginzburg, Victor},
title = {Nil-{H}ecke algebras and {W}hittaker {$\mathcal D$}-modules},
booktitle = {Lie Groups, Geometry, and Representation Theory},
series = {Progr. Math.},
volume = {326},
pages = {137--184},
publisher = {Birkhäuser/Springer, Cham},
year = {2018},
mrclass = {20G20 (14F10 16S32 17B20 20C08)},
mrnumber = {3890208},
mrreviewer = {Willem Adriaan de Graaf},
zblnumber = {1455.20030},
} -
[kt1]
M. Kashiwara and T. Tanisaki, "Kazhdan-Lusztig conjecture for affine Lie algebras with negative level," Duke Math. J., vol. 77, iss. 1, pp. 21-62, 1995.
@ARTICLE{kt1,
author = {Kashiwara, Masaki and Tanisaki, Toshiyuki},
title = {Kazhdan-{L}usztig conjecture for affine {L}ie algebras with negative level},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {77},
year = {1995},
number = {1},
pages = {21--62},
issn = {0012-7094},
mrclass = {17B67 (17B10)},
mrnumber = {1317626},
mrreviewer = {Alex Jay Feingold},
doi = {10.1215/S0012-7094-95-07702-3},
url = {https://doi.org/10.1215/S0012-7094-95-07702-3},
zblnumber = {0829.17020},
} -
@BOOK{htt,
author = {Lurie, Jacob},
title = {Higher Topos Theory},
series = {Ann. of Math. Stud.},
volume = {170},
publisher = {Princeton Univ. Press, Princeton, NJ},
year = {2009},
pages = {xviii+925},
isbn = {978-0-691-14049-0; 0-691-14049-9},
mrclass = {18-02 (18B25 18E35 18G30 18G55 55U40)},
mrnumber = {2522659},
mrreviewer = {Mark Hovey},
doi = {10.1515/9781400830558},
url = {https://doi.org/10.1515/9781400830558},
zblnumber = {1175.18001},
} -
[higheralgebra] J. Lurie, Higher algebra, 2012.
@MISC{higheralgebra,
author = {Lurie, Jacob},
title = {Higher algebra},
note = {available on author's website},
year = {2012},
} -
[mirkovic-vilonen]
I. Mirković and K. Vilonen, "Geometric Langlands duality and representations of algebraic groups over commutative rings," Ann. of Math. (2), vol. 166, iss. 1, pp. 95-143, 2007.
@ARTICLE{mirkovic-vilonen,
author = {Mirković,
I. and Vilonen, K.},
title = {Geometric {L}anglands duality and representations of algebraic groups over commutative rings},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {166},
year = {2007},
number = {1},
pages = {95--143},
issn = {0003-486X},
mrclass = {22E55 (11R39 20G05)},
mrnumber = {2342692},
mrreviewer = {Peter Fiebig},
doi = {10.4007/annals.2007.166.95},
url = {https://doi.org/10.4007/annals.2007.166.95},
zblnumber = {1138.22013},
} -
[mirkovic-vilonen-but-not-that-one]
I. Mirković and K. Vilonen, "Characteristic varieties of character sheaves," Invent. Math., vol. 93, iss. 2, pp. 405-418, 1988.
@ARTICLE{mirkovic-vilonen-but-not-that-one,
author = {Mirković,
I. and Vilonen, K.},
title = {Characteristic varieties of character sheaves},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {93},
year = {1988},
number = {2},
pages = {405--418},
issn = {0020-9910},
mrclass = {20G05 (22E47)},
mrnumber = {0948107},
mrreviewer = {Bhama Srinivasan},
doi = {10.1007/BF01394339},
url = {https://doi.org/10.1007/BF01394339},
zblnumber = {0683.22012},
} -
[opers]
S. Raskin, "A geometric proof of the Feigin-Frenkel theorem," Represent. Theory, vol. 16, pp. 489-512, 2012.
@ARTICLE{opers,
author = {Raskin, Sam},
title = {A geometric proof of the {F}eigin-{F}renkel theorem},
journal = {Represent. Theory},
fjournal = {Representation Theory. An Electronic Journal of the Amer. Math. Soc.},
volume = {16},
year = {2012},
pages = {489--512},
mrclass = {17B65 (14L24 81R10)},
mrnumber = {2972556},
mrreviewer = {Volodymyr Mazorchuk},
doi = {10.1090/S1088-4165-2012-00417-4},
url = {https://doi.org/10.1090/S1088-4165-2012-00417-4},
zblnumber = {1302.17035},
} -
[chiralcats] S. Raskin, Chiral categories, 2015.
@MISC{chiralcats,
author = {Raskin, Sam},
title = {Chiral categories},
note = {available on author's website},
year = {2015},
zblnumber = {07374911},
} -
[dmod] S. Raskin, $D$-modules on infinite dimensional varieties, 2015.
@MISC{dmod,
author = {Raskin, Sam},
note = {available on author's website},
title = {$D$-modules on infinite dimensional varieties},
year = {2015},
zblnumber = {},
} -
@BOOK{cpsii,
author = {Raskin, Sam D.},
title = {Chiral Principal Series Categories},
note = {Ph.D. {T}hesis, Harvard Univ.},
year = {2014},
pages = {340},
isbn = {978-1321-02173-8},
mrclass = {Thesis},
url = {http://nrs.harvard.edu/urn-3:HUL.InstRepos:12274305},
mrnumber = {3251357},
zblnumber = {},
} -
[methods] S. Raskin, Homological methods in semi-infinite contexts, 2019.
@MISC{methods,
author = {Raskin, Sam},
title = {Homological methods in semi-infinite contexts},
note = {available on author's website},
year = {2019},
zblnumber = {},
} -
[b-fn]
S. Raskin, "A generalization of the $b$-function lemma," Compos. Math., vol. 157, iss. 10, pp. 2199-2214, 2021.
@ARTICLE{b-fn,
author = {Raskin, Sam},
title = {A generalization of the {$b$}-function lemma},
journal = {Compos. Math.},
fjournal = {Compositio Mathematica},
volume = {157},
year = {2021},
number = {10},
pages = {2199--2214},
issn = {0010-437X},
mrclass = {14F10 (17B55 32C38)},
mrnumber = {4311556},
doi = {10.1112/S0010437X21007491},
url = {https://doi.org/10.1112/S0010437X21007491},
zblnumber = {},
} -
[whit]
S. Raskin, "$\mathcal W$-algebras and Whittaker categories," Selecta Math. (N.S.), vol. 27, iss. 3, p. 46, 2021.
@ARTICLE{whit,
author = {Raskin, Sam},
title = {{$\mathcal W$}-algebras and {W}hittaker categories},
journal = {Selecta Math. (N.S.)},
fjournal = {Selecta Mathematica. New Series},
volume = {27},
year = {2021},
number = {3},
pages = {Paper No. 46, 114},
issn = {1022-1824},
mrclass = {17B67 (22E57)},
mrnumber = {4273643},
doi = {10.1007/s00029-021-00641-6},
url = {https://doi.org/10.1007/s00029-021-00641-6},
zblnumber = {07364461},
}