On a question of Külshammer for representations of finite groups in reductive groups

2015/05/02 by Michael Bate, Bate, Michael, Benjamin Martin +3
Mathematics · #20C20 #20G15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20C20 #msc:20G15

paper · pdf · doi:10.48550/arxiv.1505.00377

5 pages. Minor changes from previous version

openalex publication_date 2015/05/02 · arxiv created 2015/05/20 · arxiv updated 2015/05/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

Let G be a simple algebraic group of type G₂ over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ₂ and an infinite family of pairwise non-conjugate homomorphisms ρ\colon Γ→ G whose restrictions to Γ₂ are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies \rm H¹(Γ,V)→ \rm H¹(Γ_p,V) induced by restriction of 1-cocycles has an infinite fibre.

Citations

• 1998 Moursund Lectures at the University of Oregon

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