We propose a new geometric model for the center of the small quantum group
using the cohomology of certain affine Springer fibers. More precisely, we
establish an isomorphism between the equivariant cohomology of affine
Spaltenstein fibers for a split element and the center of the deformed graded
modules for the small quantum group. We also obtain an embedding from the
invariant part of the nonequivariant cohomology under the action of the
extended affine Weyl group to the invariant part of the center of the small
quantum group under Langlands dual group action, which we conjecture to be an
isomorphism. Finally, we give a dimension formula for the invariants on the
cohomology side, thus providing a lower bound for the dimension of the center.
Beschreibung
A geometric realization of the center of the small quantum group
%0 Generic
%1 bezrukavnikov2022geometric
%A Bezrukavnikov, Roman
%A Alvarez, Pablo Boixeda
%A Shan, Peng
%A Vasserot, Eric
%D 2022
%K Center springer
%T A geometric realization of the center of the small quantum group
%U http://arxiv.org/abs/2205.05951
%X We propose a new geometric model for the center of the small quantum group
using the cohomology of certain affine Springer fibers. More precisely, we
establish an isomorphism between the equivariant cohomology of affine
Spaltenstein fibers for a split element and the center of the deformed graded
modules for the small quantum group. We also obtain an embedding from the
invariant part of the nonequivariant cohomology under the action of the
extended affine Weyl group to the invariant part of the center of the small
quantum group under Langlands dual group action, which we conjecture to be an
isomorphism. Finally, we give a dimension formula for the invariants on the
cohomology side, thus providing a lower bound for the dimension of the center.
@misc{bezrukavnikov2022geometric,
abstract = {We propose a new geometric model for the center of the small quantum group
using the cohomology of certain affine Springer fibers. More precisely, we
establish an isomorphism between the equivariant cohomology of affine
Spaltenstein fibers for a split element and the center of the deformed graded
modules for the small quantum group. We also obtain an embedding from the
invariant part of the nonequivariant cohomology under the action of the
extended affine Weyl group to the invariant part of the center of the small
quantum group under Langlands dual group action, which we conjecture to be an
isomorphism. Finally, we give a dimension formula for the invariants on the
cohomology side, thus providing a lower bound for the dimension of the center.},
added-at = {2022-05-13T16:42:14.000+0200},
author = {Bezrukavnikov, Roman and Alvarez, Pablo Boixeda and Shan, Peng and Vasserot, Eric},
biburl = {https://www.bibsonomy.org/bibtex/25b67a35c2d502c14496eb8bf9d718756/dragosf},
description = {A geometric realization of the center of the small quantum group},
interhash = {6d8eca547bea3d48f29826ecd0171b34},
intrahash = {5b67a35c2d502c14496eb8bf9d718756},
keywords = {Center springer},
note = {cite arxiv:2205.05951Comment: 52 pages},
timestamp = {2022-05-13T16:42:14.000+0200},
title = {A geometric realization of the center of the small quantum group},
url = {http://arxiv.org/abs/2205.05951},
year = 2022
}