Generic representations of finite general linear groups in cross characteristic

Aurélien Djament; Thomas Gaujal

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arXiv · 2305.02581

Generic representations of finite general linear groups in cross characteristic

Aurélien Djament·Thomas Gaujal

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Abstract

We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We obtain especially a classification of such simple representations, what allows to prove a conjecture of Djament-Touz{\'e}-Vespa on dimensions taken by such a functor.

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Aurélien Djament, Thomas Gaujal. 2023-05-04. Generic representations of finite general linear groups in cross characteristic. https://arxiv.org/abs/2305.02581

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