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Orthosymplectic Satake equivalence, II

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arxiv 2207.03115 v3 pith:EXJDG52B submitted 2022-07-07 math.RT hep-thmath.AGmath.QA

classification math.RThep-thmath.AGmath.QA
keywords equivalencearxivorthosymplecticsupergroupsaffinecalledcasecategory
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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.

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