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Mirabolic Satake equivalence and supergroups
- Part of
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- Journal:
- Compositio Mathematica / Volume 157 / Issue 8 / August 2021
- Published online by Cambridge University Press:
- 22 July 2021, pp. 1724-1765
- Print publication:
- August 2021
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- Article
- Export citation
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We construct a mirabolic analogue of the geometric Satake equivalence. We also prove an equivalence that relates representations of a supergroup to the category of
$\operatorname{GL}(N-1,{\mathbb {C}}[\![t]\!])$-equivariant perverse sheaves on the affine Grassmannian of 
$\operatorname{GL}_N$. We explain how our equivalences fit into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.
