Mirabolic Satake equivalence and supergroups

Alexander Braverman; Michael Finkelberg; Victor Ginzburg; Roman Travkin

doi:10.1112/S0010437X21007387

Mirabolic Satake equivalence and supergroups

Alexander Braverman
, Michael Finkelberg
, Victor Ginzburg
, Roman Travkin

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1724-1765
Number of pages	42
Journal	Compositio Mathematica
Volume	157
Issue number	8
DOIs	https://doi.org/10.1112/S0010437X21007387
State	Published - Aug 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 The Author(s).

Keywords

Satake equivalence
mirabolic affine Grassmannian
supergroups

Access to Document

10.1112/S0010437X21007387

Cite this

@article{e12dcdc5fec54a4d86852f8c766f1845,

title = "Mirabolic Satake equivalence and supergroups",

abstract = "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.",

keywords = "Satake equivalence, mirabolic affine Grassmannian, supergroups",

author = "Alexander Braverman and Michael Finkelberg and Victor Ginzburg and Roman Travkin",

note = "Publisher Copyright: {\textcopyright} 2021 The Author(s).",

year = "2021",

month = aug,

doi = "10.1112/S0010437X21007387",

language = "אנגלית",

volume = "157",

pages = "1724--1765",

journal = "Compositio Mathematica",

issn = "0010-437X",

publisher = "Cambridge University Press",

number = "8",

}

TY - JOUR

T1 - Mirabolic Satake equivalence and supergroups

AU - Braverman, Alexander

AU - Finkelberg, Michael

AU - Ginzburg, Victor

AU - Travkin, Roman

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Satake equivalence

KW - mirabolic affine Grassmannian

KW - supergroups

UR - https://www.scopus.com/pages/publications/85123722255

U2 - 10.1112/S0010437X21007387

DO - 10.1112/S0010437X21007387

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85123722255

SN - 0010-437X

VL - 157

SP - 1724

EP - 1765

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 8

ER -

Mirabolic Satake equivalence and supergroups

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this