Low dimensional projective indecomposable modules for Chevalley groups in defining characteristic

2012/02/06 by Alexandre Zalesski, Alexandre E. Zalesski, Zalesski, Alexandre E.
Mathematics · #20C20 #20C33 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20C20 #msc:20C33

paper · pdf · doi:10.48550/arxiv.1202.1308

arxiv created 2012/02/06 · openalex publication_date 2012/02/06 · arxiv updated 2012/02/08 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

The paper studies lower bounds for the dimensions of projective indecomposable modules for Chevalley groups G in defining characteristic p. The main result extending earlier one by Malle and Weigel (2008) determines the modules in question of dimension equal to the order of a Sylow p-subgroup of G. We also substantially generalize a result by Ballard (1978) on lower bounds for the dimensions of projective indecomposable modules and find lower bounds in some cases where Ballard's bounds are vacuous.

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