Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution

Abstract

We study the effect of Alvis-Curtis duality on the unipotent representations of GLn(q) in non-defining characteristic ℓ. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves both ℓ and the order of q modulo ℓ.