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Pré-Publication, Document De Travail Année : 2023

Categorical actions on unipotent representations of finite classical groups

Résumé

We review the categorical representation of a Kac-Moody algebra on unipotent representations of finite unitary groups in non-defining characteristic given by the authors. Then, we extend this construction to finite reductive groups of types B or C, in non-defining characteristic. We show that the decategorified representation is isomorphic to a direct sum of level 2 Fock spaces. We deduce that the Harish-Chandra branching graph coincides with the crystal graph of these Fock spaces. We also obtain derived equivalences between blocks, yielding Broue's abelian defect group conjecture for unipotent l-blocks at linear primes.

Dates et versions

hal-04223858 , version 1 (30-09-2023)

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Olivier Dudas, Michela Varagnolo, Eric Vasserot. Categorical actions on unipotent representations of finite classical groups. 2023. ⟨hal-04223858⟩
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