Mirabolic Satake equivalence and supergroups

被引：8

作者：

Braverman, Alexander ^{[1
,2
]}

Finkelberg, Michael ^{[2
,3
,4
]}

Ginzburg, Victor ^{[5
]}

Travkin, Roman ^{[2
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[2] Skolkovo Inst Sci & Technol, Moscow, Russia

[3] Natl Res Univ Higher Sch Econ, Dept Math, Moscow 119048, Russia

[4] Inst Informat Transmiss Problems, Moscow, Russia

[5] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

COMPOSITIO MATHEMATICA | 2021年 / 157卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Satake equivalence; mirabolic affine Grassmannian; supergroups; REPRESENTATIONS; CATEGORY; DUALITY;

D O I：

10.1112/S0010437X21007387

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a mirabolic analogue of the geometric Satake equivalence. We also prove an equivalence that relates representations of a supergroup to the category of GL(N - 1, C[[t]])-equivariant perverse sheaves on the affine Grassmannian of GLN. We explain how our equivalences fit into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.

引用

页码：1724 / 1765

页数：43

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