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.
|Number of pages||14|
|Journal||Forum of Mathematics, Sigma|
|Publication status||Accepted/In press - 15 Dec 2021|
- G-complete reducibility
- overgroups of regular unipotent elements
- finite groups of Lie type