Overgroups of regular unipotent elements in reductive groups
Group Theory
2023-06-22 v3
Abstract
We study reductive subgroups of a reductive linear algebraic group -- possibly non-connected -- such that contains a regular unipotent element of . We show that under suitable hypotheses, such subgroups are -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.
Cite
@article{arxiv.2107.01925,
title = {Overgroups of regular unipotent elements in reductive groups},
author = {Michael Bate and Ben Martin and Gerhard Roehrle},
journal= {arXiv preprint arXiv:2107.01925},
year = {2023}
}
Comments
13 pages; v2 added Corollary 5.2; v3 final version; some references added, further small changes; to appear in Forum of Mathematics, Sigma