Categorical actions on unipotent representations of finite unitary groups

O. Dudas; M. Varagnolo; E. Vasserot

doi:10.1007/s10240-019-00104-x

Article

Categorical actions on unipotent representations of finite unitary groups

O. Dudas ¹; M. Varagnolo ¹; E. Vasserot ¹

¹

Publications Mathématiques de l'IHÉS, Volume 129 (2019), pp. 129-197

Abstract

Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified representation is naturally isomorphic to a direct sum of level 2 Fock spaces. From our construction we deduce that the Harish-Chandra branching graph coincides with the crystal graph of these Fock spaces, solving a recent conjecture of Gerber-Hiss-Jacon. We also obtain derived equivalences between blocks, yielding Broué’s abelian defect group conjecture for unipotent $ℓ$ -blocks at linear primes $ℓ$ .

Received: 2016-01-05
Accepted: 2019-02-27
Online First: 2019-03-08
Published online: 2019-06-01

MR

DOI: 10.1007/s10240-019-00104-x

Author's affiliations:

O. Dudas ¹; M. Varagnolo ¹; E. Vasserot ¹

¹

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     title = {Categorical actions on unipotent representations of finite unitary groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {129--197},
     year = {2019},
     publisher = {Springer Berlin Heidelberg},
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O. Dudas; M. Varagnolo; E. Vasserot. Categorical actions on unipotent representations of finite unitary groups. Publications Mathématiques de l'IHÉS, Volume 129 (2019), pp. 129-197. doi: 10.1007/s10240-019-00104-x

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