Irreducible A1 subgroups of exceptional algebraic groups

Adam R. Thomas*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
254 Downloads (Pure)


A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible A1 subgroups of exceptional algebraic groups G. Consequences are given concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible A1 subgroups are determined by their composition factors on the adjoint module of G.

Original languageEnglish
Pages (from-to)240-296
Number of pages57
JournalJournal of Algebra
Early online date9 Nov 2015
Publication statusPublished - 1 Feb 2016


  • A subgroups
  • Algebraic groups
  • Complete reducibility
  • G-irreduciblitly
  • Subgroups structure


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