  We study the effect of Alvis-Curtis duality on the unipotent representations
of $\mathrm{GL}_n(q)$ in non-defining characteristic $\ell$. 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 $\ell$ and the order of $q$ modulo $\ell$.
