Bounds on the number of simple modules in blocks of finite groups of Lie type

2019/07/24 by Ruwen Hollenbach, Hollenbach, Ruwen
Mathematics · #20C15 #20C33 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C15 #msc:20C33

paper · pdf · doi:10.48550/arxiv.1907.10353

19 pages

arxiv created 2019/07/24 · openalex publication_date 2019/07/24 · arxiv updated 2019/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a simple, simply connected linear algebraic group of exceptional type defined over \mathbbF_q with Frobenius endomorphism F: G → G. In this work we give upper bounds on the number of simple modules in the quasi-isolated ℓ-blocks of G^F and G^F/Z(G^F) when ℓ is bad for G.

Related

• Exceptional representations of simple algebraic groups in prime characteristic
• Simple endotrivial modules for linear, unitary and exceptional groups
• Rationality of blocks of quasi-simple finite groups
• Quasi-isolated blocks and Brauer's height zero conjecture
• Source Algebras of Blocks, Sources of Simple Modules, and a Conjecture of Feit