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

详细信息    查看全文

• 作者：Michael Bate ; Benjamin Martin ; Gerhard Röhrle
• 刊名：Israel Journal of Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：214
• 期：1
• 页码：463-470
• 全文大小：160 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511
• 卷排序：214

文摘

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(Γ_p, V) induced by restriction of 1-cocycles has an infinite fibre.