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arXiv · 1611.07373

Modular irreducibility of cuspidal unipotent characters

Olivier Dudas·Gunter Malle
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Abstract

We prove a long-standing conjecture of Geck which predicts that cuspidal unipotent characters remain irreducible after $\ell$-reduction. To this end, we construct a progenerator for the category of representations of a finite reductive group coming from generalised Gelfand--Graev representations. This is achieved by showing that cuspidal representations appear in the head of generalised Gelfand--Graev representations attached to cuspidal unipotent classes, as defined and studied in \cite{GM96}.

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Olivier Dudas, Gunter Malle. 2016-11-22. Modular irreducibility of cuspidal unipotent characters. https://arxiv.org/abs/1611.07373

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