Overgroups of regular unipotent elements in reductive groups

Abstract

We study reductive subgroups $H$ of a reductive linear algebraic group $G$ -- possibly non-connected -- such that $H$ contains a regular unipotent element of $G$. We show that under suitable hypotheses, such subgroups are $G$-irreducible in the sense of Serre. This generalizes results of Malle, Testerman and Zalesski. We obtain analogous results for Lie algebras and for finite groups of Lie type. Our proofs are short, conceptual and uniform.

13 pages; v2 added Corollary 5.2; v3 final version; some references added, further small changes; to appear in Forum of Mathematics, Sigma

References in corpus (1)

• Semisimplification for Subgroups of Reductive Algebraic Groups