Equivariant derived category of a reductive group as a categorical center
Representation Theory
2024-06-13 v3 Algebraic Geometry
Abstract
We prove that the adjoint equivariant derived category of a reductive group is equivalent to the appropriately defined monoidal center of the torus-equivariant version of the Hecke category. We use this to give new proofs, independent of sheaf-theoretic set up, of the fact that the Drinfeld center of the abelian Hecke category is equivalent to the abelian category of unipotent character sheaves; and of a characterization of strongly-central sheaves on the torus.
Keywords
Cite
@article{arxiv.2305.02980,
title = {Equivariant derived category of a reductive group as a categorical center},
author = {Roman Bezrukavnikov and Andrei Ionov and Kostiantyn Tolmachov and Yakov Varshavsky},
journal= {arXiv preprint arXiv:2305.02980},
year = {2024}
}