Orthosymplectic Satake equivalence, II

TL;DR

This paper establishes a categorical equivalence linking representations of a degenerate orthosymplectic supergroup with twisted D-modules on a mirabolic affine Grassmannian, extending to quantum and exceptional supergroups.

Contribution

It proves a new equivalence relating supergroup representations to geometric objects, and discusses potential extensions to quantum and exceptional supergroups.

Findings

Proves an equivalence between supergroup representations and D-modules on affine Grassmannian.

Extends the equivalence to quantum supergroups.

Discusses conjectural extensions to exceptional supergroups.

Abstract

This is a companion paper of arXiv:1909.11492 and arXiv:1912.01930. We prove an equivalence relating representations of a degenerate orthosymplectic supergroup with the category of twisted $Sp(2n,{\mathbb C}[\![t]\!])$-equivariant $D$-modules on the so called mirabolic affine Grassmannian of $Sp(2n)$. We also discuss (conjectural) extension of this equivalence to the case of quantum supergroups and to some exceptional supergroups.