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arXiv · 1510.00997

Non-separability and complete reducibility: $E_n$ examples with an application to a question of K\"ulshammer

Tomohiro Uchiyama
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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 K\"ulshammer on representations of finite groups in reductive groups. We also consider a rationality problem for $G$-complete reducibility and a problem concerning conjugacy classes.

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Tomohiro Uchiyama. 2015-10-04. Non-separability and complete reducibility: $E_n$ examples with an application to a question of K\"ulshammer. https://arxiv.org/abs/1510.00997

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