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Categorical actions on unipotent representations of finite unitary groups
Categorical actions on unipotent representations of finite unitary groups
- 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 $ .
- Subjects :
- Pure mathematics
Conjecture
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]
Direct sum
General Mathematics
010102 general mathematics
Unipotent
01 natural sciences
Unitary state
Fock space
Number theory
0103 physical sciences
010307 mathematical physics
0101 mathematics
Abelian group
Mathematics::Representation Theory
Categorical variable
ComputingMilieux_MISCELLANEOUS
Mathematics
Subjects
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⟩