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Reducible subgroups of exceptional algebraic groups

Litterick, Alastair J and Thomas, Adam R (2019) 'Reducible subgroups of exceptional algebraic groups.' Journal of Pure and Applied Algebra, 223 (6). 2489 - 2529. ISSN 0022-4049

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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 G-cr 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.

Item Type: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 05 Sep 2019 09:44
Last Modified: 05 Sep 2019 10:15

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