Orthosymplectic Satake equivalence, II

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.

v2: section 3.2 added. v3: some corrections; references updated