Reducible subgroups of exceptional algebraic groups

Alastair Litterick, Adam Thomas

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Let G be a simple algebraic group over an algebraically closed field. A closed subgroup H of G is called G-completely reducible (G-cr) if, whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi factor of P. In this paper we complete the classification of connected Gcr subgroups when G has exceptional type, by determining the L0-irreducible connected reductive subgroups for each simple classical factor L0 of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type F4 and various properties thereof. This work complements results of Lawther, Liebeck, Seitz and Testerman, and is vital in classifying non-G-cr reductive subgroups, a project being undertaken by the authors elsewhere.
Original languageEnglish
Pages (from-to)2489-2529
Number of pages41
JournalJournal of Pure and Applied Algebra
Issue number6
Early online date13 Sept 2018
Publication statusPublished - 1 Jun 2019


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