Representations of finite special linear groups in non-defining characteristic

2008/10/05 by Alexander Kleshchev, Alexander S. Kleshchev, Kleshchev, Alexander S. +2
Computer Science · Mathematics · #20C20 #20E28 #20G40 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C20 #msc:20E28 #msc:20G40

paper · pdf · doi:10.48550/arxiv.0810.0849

24 pages. Advances in Mathematics, to appear

arxiv created 2008/10/05 · openalex publication_date 2008/10/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of GL_n(q) on restriction to SL_n(q). Combined with a recent result of C. Bonnafe, this yields a canonical labeling for irreducible ℓ-modular representations of SL_n(q), where (ℓ,q)=1. As an application, we classify for the first time complex representations of SL_n(q) whose reductions modulo ℓ are irreducible.

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