Kazhdan-Lusztig conjecture via zastava spaces

被引：0

作者：

Braverman, Alexander ^{[1
,2
,3
]}

Finkelberg, Michael ^{[3
,4
,5
]}

Nakajima, Hiraku ^{[6
,7
]}

机构：

[1] Univ Toronto, Dept Math, Waterloo, ON N2L 2Y5, Canada

[2] Univ Toronto, Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada

[3] Skolkovo Inst Sci & Technol, Bolshoi Bulvar 30,Bld 1, Moscow 121205, Russia

[4] Natl Res Univ Higher Sch Econ, Dept Math, 6 Usacheva St, Moscow 119048, Russia

[5] Inst Informat Transmiss Problems, Bolshoi Karetnyi 19, Moscow 127051, Russia

[6] Univ Tokyo, Kavli Inst Phys & Math Univ WPI, 5-1-5 Kashiwanoha, Kashiwa, Chiba 2778583, Japan

[7] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2022年 / 2022卷 / 787期

基金：

日本学术振兴会;

关键词：

KOSZUL DUALITY; QUIVER VARIETIES; LOCALIZATION; CATEGORY; ALGEBRAS; MODULES;

D O I：

10.1515/crelle-2022-0013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deduce the Kazhdan-Lusztig conjecture on the multiplicities of simple modules over a simple complex Lie algebra in Verma modules in category O from the equivariant geometric Satake correspondence and the analysis of torus fixed points in zastava spaces. We make similar speculations for the affine Lie algebras and W-algebras.

引用

页码：45 / 78

页数：34

共 38 条

[21] A note on a symplectic structure on the space of G-monopoles
Finkelberg, M
Kuznetsov, A
Markarian, N
Mirkovic, I
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 201 (02) : 411 - 421
[22] A Note on a Symplectic Structure on the Space of G-Monopoles (vol 201, pg 411, 1999)
Finkelberg, Michael
Kuznetsov, Alexander
Markarian, Nikita
Mirkovic, Ivan
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 334 (02) : 1153 - 1155
[23] Frenkel E., 2009, REPRESENT THEOR, V13, P470
[24] Gaitsgory D., 2005, NOTION CATEGORY OVER
[25] Sheaves of categories and the notion of 1-affineness
Gaitsgory, Dennis
[J]. STACKS AND CATEGORIES IN GEOMETRY, TOPOLOGY, AND ALGEBRA, 2015, 643 : 127 - 225
[26] Ginzburg V., 1993, Internat. Math. Res. Notices (IMRN), V1993, P67, DOI DOI 10.1155/S1073792893000078
[27] Goresky M, 1998, INVENT MATH, V131, P25
[28] Kazhdan-Lusztig conjecture for affine lie algebras with negative level .2. Nonintegral case
Kashiwara, M
Tanisaki, T
[J]. DUKE MATHEMATICAL JOURNAL, 1996, 84 (03) : 771 - 813
[29] Kashiwara M., 1998, MIKIO SATO GREAT JAP, V2, P779
[30] MONODROMIC SYSTEMS ON AFFINE FLAG MANIFOLDS
LUSZTIG, G
[J]. PROCEEDINGS OF THE ROYAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1994, 445 (1923): : 231 - 246

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