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We study the effect of Alvis-Curtis duality on the unipotent representationsof $\mathrm{GL}_n(q)$ in non-defining characteristic $\ell$. We show that thepermutation induced on the simple modules can be expressed in terms of ageneralization of the Mullineux involution on the set of all partitions, whichinvolves both $\ell$ and the order of $q$ modulo $\ell$.

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