Overgroups of regular unipotent elements in reductive groups

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

*Corresponding author for this work

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We study reductive subgroups H of a reductive linear algebraic group G - possibly nonconnected - 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 generalises 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
Article numbere13
Number of pages13
JournalForum of Mathematics, Sigma
Early online date24 Feb 2022
Publication statusPublished - 24 Feb 2022

Bibliographical note

Acknowledgments. We thank Donna Testerman for comments on an earlier version of the paper, and the referee for several suggestions which have improved the exposition.


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


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