English

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 GL(N1,C[ ⁣[t] ⁣])GL(N-1,{\mathbb C}[\![t]\!])-equivariant perverse sheaves on the affine Grassmannian of GLNGL_N. 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

R2 v1 2026-06-23T11:25:28.764Z