Equivariant derived category of a reductive group as a categorical center
Abstract
We prove that the adjoint equivariant derived category of a reductive group $G$ is equivalent to the appropriately defined monoidal center of the torusequivariant version of the Hecke category. We use this to give new proofs, independent of sheaftheoretic 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 stronglycentral sheaves on the torus.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.02980
 arXiv:
 arXiv:2305.02980
 Bibcode:
 2023arXiv230502980B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry