Mirabolic Satake equivalence and supergroups
Representation Theory
2023-06-22 v3 High Energy Physics - Theory
Algebraic Geometry
Quantum Algebra
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 -equivariant perverse sheaves on the affine Grassmannian of . We explain how our equivalences fit into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.
Cite
@article{arxiv.1909.11492,
title = {Mirabolic Satake equivalence and supergroups},
author = {Alexander Braverman and Michael Finkelberg and Victor Ginzburg and Roman Travkin},
journal= {arXiv preprint arXiv:1909.11492},
year = {2023}
}
Comments
v2: 48 pages, a few minor corrections. v3: the final version published in Compositio Mathematica