Communications in Number Theory and Physics

Volume 16 (2022)

Number 4

Orthosymplectic Satake equivalence

Pages: 695 – 732

DOI: https://dx.doi.org/10.4310/CNTP.2022.v16.n4.a2

Authors

Alexander Braverman (Department of Mathematics, University of Toronto, Quebec, Canada; Perimeter Institute of Theoretical Physics, Waterloo, Ontario, Canada; and Skolkovo Institute of Science and Technology, Moscow, Russia)

Michael Finkelberg (Department of Mathematics, National Research University Higher School of Economics, Moscow, Russia; Skolkovo Institute of Science and Technology, Moscow, Russia; and Institute for the Information Transmission Problems, Moscow, Russia)

Roman Travkin (Skolkovo Institute of Science and Technology, Moscow, Russia)

Abstract

This is a companion paper of [BFGT]. We prove an equivalence relating representations of a degenerate orthosymplectic supergroup with the category of $\mathrm{SO}(N-1,\mathbb{C} [\![t]\!])$-equivariant perverse sheaves on the affine Grassmannian of $\mathrm{SO}_N$. We explain how this equivalence fits into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.

Keywords

Satake equivalence, affine Grassmannian, supergroups

2010 Mathematics Subject Classification

14D24, 14F99, 14M15, 17B20

Full Text (PDF format)

To the memory of Elena V. Glivenko

A.B. was partially supported by NSERC.

M.F. was partially funded within the framework of the HSE University Basic Research Program and the Russian Academic Excellence Project ‘5-100’.

Received 2 June 2020

Accepted 24 August 2022

Published 21 October 2022