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Mirabolic Satake equivalence and supergroups (1909.11492v3)
Published 25 Sep 2019 in math.RT, hep-th, math.AG, and math.QA
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 $GL_N$. We explain how our equivalences fit into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.