Equivariant derived category of a reductive group as a categorical center

Fuente: arXiv
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Main Authors: Bezrukavnikov, Roman, Ionov, Andrei, Tolmachov, Kostiantyn, Varshavsky, Yakov
Format: Preprint
Published: 2023
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author Bezrukavnikov, Roman
Ionov, Andrei
Tolmachov, Kostiantyn
Varshavsky, Yakov
author_facet Bezrukavnikov, Roman
Ionov, Andrei
Tolmachov, Kostiantyn
Varshavsky, Yakov
contents We prove that the adjoint equivariant derived category of a reductive group $G$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_02980
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Equivariant derived category of a reductive group as a categorical center
Bezrukavnikov, Roman
Ionov, Andrei
Tolmachov, Kostiantyn
Varshavsky, Yakov
Representation Theory
Algebraic Geometry
We prove that the adjoint equivariant derived category of a reductive group $G$ 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.
title Equivariant derived category of a reductive group as a categorical center
topic Representation Theory
Algebraic Geometry
url https://arxiv.org/abs/2305.02980