Geodesic
Article
Categorical actions on unipotent representations of finite unitary groups
Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 129-197

Voir la notice de l'article provenant de la source Numdam

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 :
Accepté le :
Première publication :
Publié le :
DOI : 10.1007/s10240-019-00104-x

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

1 
@article{PMIHES_2019__129__129_0,
     author = {Dudas, O. and Varagnolo, M. and Vasserot, E.},
     title = {Categorical actions on unipotent representations of finite unitary groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {129--197},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {129},
     year = {2019},
     doi = {10.1007/s10240-019-00104-x},
     mrnumber = {3949029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00104-x/}
}
TY  - JOUR
AU  - Dudas, O.
AU  - Varagnolo, M.
AU  - Vasserot, E.
TI  - Categorical actions on unipotent representations of finite unitary groups
JO  - Publications Mathématiques de l'IHÉS
PY  - 2019
SP  - 129
EP  - 197
VL  - 129
PB  - Springer Berlin Heidelberg
PP  - Berlin/Heidelberg
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00104-x/
DO  - 10.1007/s10240-019-00104-x
LA  - en
ID  - PMIHES_2019__129__129_0
ER  - 
%0 Journal Article
%A Dudas, O.
%A Varagnolo, M.
%A Vasserot, E.
%T Categorical actions on unipotent representations of finite unitary groups
%J Publications Mathématiques de l'IHÉS
%D 2019
%P 129-197
%V 129
%I Springer Berlin Heidelberg
%C Berlin/Heidelberg
%U http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00104-x/
%R 10.1007/s10240-019-00104-x
%G en
%F PMIHES_2019__129__129_0
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

Cité par Sources :