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

[1] [Anonymous], 2013, SYMMETRIES INTEGRABL
[2] [Anonymous], 2006, INT C MATHEMATICIANS
[3] Arakawa T, 2007, INVENT MATH, V169, P219, DOI 10.1007/s00222-007-0046-1
[4] Singular support of coherent sheaves and the geometric Langlands conjecture
Arinkin, D.
Gaitsgory, D.
[J]. SELECTA MATHEMATICA-NEW SERIES, 2015, 21 (01): : 1 - 199
[5] Modules over the small quantum group and semi-infinite flag manifold
Arkhipov, S
Bezrukavnikov, R
Braverman, A
Gaitscory, D
Mikovic, I
[J]. TRANSFORMATION GROUPS, 2005, 10 (3-4) : 279 - 362
[6] Another realization of the category of modules over the small quantum group
Arkhipov, S
Gaitsgory, D
[J]. ADVANCES IN MATHEMATICS, 2003, 173 (01) : 114 - 143
[7] Koszul duality patterns in representation theory
Beilinson, A
Ginzburg, V
Soergel, W
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (02) : 473 - 527
[8] Beilinson A., 1993, Seminar, V16, P1
[9] A DG guide to Voevodsky's motives
Beilinson, Alexander
Vologodsky, Vadim
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2008, 17 (06) : 1709 - 1787
[10] Bezrukavnikov R, 2013, REPRESENT THEOR, V17, P1

← 1 2 3 4 →