Mirabolic Satake equivalence and supergroups

Abstract

We construct a mirabolic analogue of the geometric Satake equivalence. We also prove an equivalence that relates representations of a supergroup with the category of $GL(N-1,\mathbb{C}[[t]])$-equivariant perverse sheaves on the affine Grassmannian of $G{L}_N$. We explain how our equivalences fit into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.

v2: 48 pages, a few minor corrections. v3: the final version published in Compositio Mathematica

Cited by in corpus (4)

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• Strongly tempered hyperspherical Hamiltonian spaces
• Hyperspherical equivariant slices and basic classical Lie superalgebras
• Duality via convolution of W-algebras