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Categorical actions on unipotent representations of finite unitary groups

Categorical actions on unipotent representations of finite unitary groups

Authors :
Michela Varagnolo
Eric Vasserot
Olivier Dudas
Analyse, Géométrie et Modélisation (AGM - UMR 8088)
CY Cergy Paris Université (CY)-Centre National de la Recherche Scientifique (CNRS)
Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG)
Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Source :
Publications Mathématiques de L'IHÉS, Publications Mathématiques de L'IHÉS, Springer Verlag, 2019, 129 (1), pp.129-197. ⟨10.1007/s10240-019-00104-x⟩
Publication Year :
2019
Publisher :
HAL CCSD, 2019.

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 Broue’s abelian defect group conjecture for unipotent $\ell $ -blocks at linear primes $\ell $ .

Details

Language :
English
ISSN :
00738301 and 16181913
Database :
OpenAIRE
Journal :
Publications Mathématiques de L'IHÉS, Publications Mathématiques de L'IHÉS, Springer Verlag, 2019, 129 (1), pp.129-197. ⟨10.1007/s10240-019-00104-x⟩
Accession number :
edsair.doi.dedup.....bcbb4c74617c8dc956ab08d748c24503
Full Text :
https://doi.org/10.1007/s10240-019-00104-x⟩