Equivariant derived category of a reductive group as a categorical center
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910483077922816 |
|---|---|
| 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 |