Geodesic
Alvis–Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\ell$.
Keywords: Mullineux involution; Alvis–Curtis duality; crystal graph; Harish-Chandra theory. 
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     title = {Alvis{\textendash}Curtis {Duality} for {Finite} {General} {Linear} {Groups} and {a~Generalized} {Mullineux} {Involution}},
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}
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Olivier Dudas; Nicolas Jacon. Alvis–Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a6/

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