Overgroups of regular unipotent elements in reductive groups

Michael Bate* (Corresponding Author), Ben Martin, Gerhard Röhrle

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Number of pages14
JournalForum of Mathematics, Sigma
Publication statusAccepted/In press - 15 Dec 2021


  • G-irreducibility
  • G-complete reducibility
  • overgroups of regular unipotent elements
  • finite groups of Lie type


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