Gaiotto conjecture for $Rep_q(GL(N-1|N))$

TL;DR

This paper proves Gaiotto's conjecture relating to the geometric Satake equivalence for the quantum supergroup $U_q({\mathfrak{gl}}(N-1|N))$, establishing a categorical equivalence via factorizable sheaves for generic q.

Contribution

It confirms Gaiotto's conjecture for the geometric Satake equivalence in the context of quantum supergroups, specifically for $U_q({\mathfrak{gl}}(N-1|N))$, using the framework of factorizable sheaves.

Findings

Proves Gaiotto's conjecture for generic q.

Establishes categorical equivalence via factorizable sheaves.

Advances understanding of quantum supergroup representations.

Abstract

We prove D.Gaiotto's conjecture about geometric Satake equivalence for quantum supergroup $U_q({\mathfrak{gl}}(N-1|N))$ for generic $q$. The equivalence goes through the category of factorizable sheaves.