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

Michael Bate, Benjamin Martin, Gerhard Rohrle

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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: 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 H1(Γ, V) → H1(Γp, V) induced by restriction of 1-cocycles has an infinite fibre.

To Burkhard Külshammer on his sixtieth birthday
Original languageEnglish
Pages (from-to)463-470
Number of pages8
JournalIsrael Journal of Mathematics
Volume214
Issue number1
DOIs
Publication statusPublished - 1 Jul 2016

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