Generic representations of finite general linear groups in cross characteristic

2023/05/03 by Aurélien Djament, Djament, Aurélien, Thomas Gaujal +1
Business, Management and Accounting · Engineering · Mathematics · #Advanced Algebra and Geometry #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Finite Group Theory Research #K-Theory and Homology (math.KT) #Optics and Image Analysis #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2305.02581

openalex publication_date 2023/05/04 · openalex created_date 2023/05/07 · openalex updated_date 2026/07/28

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-Touzé-Vespa on dimensions taken by such a functor.

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