Untwisted Gaiotto equivalence

Abstract

This is a successive paper of [5]. We prove an equivalence between the category of finite-dimensional representations of degenerate supergroup GL_(M|N) and the category of (GLM(O)⋉UM,N(F),χM,N)-equivariant D-modules on GrN. We also prove that we can realize the category of finite-dimensional representations of degenerate supergroup GL_(M|N) as a category of D-modules on the mirabolic subgroup MirL(F) with certain equivariant conditions for any L bigger than N and M.