Categorical actions on unipotent representations of finite unitary groups

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

doi:10.1007/s10240-019-00104-x

Article

Categorical actions on unipotent representations of finite unitary groups

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

¹

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

Résumé

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 $ℓ$ .

Reçu le : 2016-01-05
Accepté le : 2019-02-27
Première publication : 2019-03-08
Publié le : 2019-06-01

MR

DOI : 10.1007/s10240-019-00104-x

Affiliations des auteurs :

Dudas, O. ¹ ; Varagnolo, M. ¹ ; Vasserot, E. 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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Dudas, O.; Varagnolo, M.; Vasserot, E. Categorical actions on unipotent representations of finite unitary groups. Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 129-197. doi: 10.1007/s10240-019-00104-x

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