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arXiv · 1706.04743

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

Olivier Dudas·Nicolas Jacon
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Abstract

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 $\ell$.

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BibTeXRIS

Olivier Dudas, Nicolas Jacon. 2017-06-15. Alvis-Curtis Duality for Finite General Linear Groups and a Generalized Mullineux Involution. https://doi.org/10.3842/sigma.2018.007

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