Orthosymplectic Satake equivalence

TL;DR

This paper establishes an equivalence between representations of a degenerate orthosymplectic supergroup and certain equivariant perverse sheaves on the affine Grassmannian, connecting to broader conjectural frameworks.

Contribution

It proves a new equivalence linking supergroup representations with geometric objects, expanding the understanding of the orthosymplectic Satake correspondence.

Findings

Established an equivalence between supergroup representations and perverse sheaves.

Connected the results to conjectural frameworks by Gaiotto and others.

Provides a geometric interpretation of supergroup representation theory.

Abstract

This is a companion paper of arXiv:1909.11492. We prove an equivalence relating representations of a degenerate orthosymplectic supergroup with the category of $SO(N-1,{\mathbb C}[\![t]\!])$-equivariant perverse sheaves on the affine Grassmannian of $SO_N$. We explain how this equivalence fits into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.