Non-separability and complete reducibility: $E_n$ examples with an application to a question of Külshammer

Abstract

Let $G$ be a simple algebraic group of type $E_n(n=6,7,8)$ defined over an algebraically closed field $k$ of characteristic $2$. We present examples of triples of closed reductive groups $H<M<G$ such that $H$ is $G$-completely reducible, but not $M$-completely reducible. As an application, we consider a question of Külshammer on representations of finite groups in reductive groups. We also consider a rationality problem for $G$-complete reducibility and a problem concerning conjugacy classes.

To appear in J. Group Theory. arXiv admin note: text overlap with arXiv:1309.3807

References in corpus (2)

• Simple Irreducible Subgroups of Exceptional Algebraic Groups
• On a question of Külshammer for representations of finite groups in reductive groups

Cited by in corpus (1)

• Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields 2