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Reducible subgroups of exceptional algebraic groups

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Litterick, Alastair and Thomas, Adam (2019) Reducible subgroups of exceptional algebraic groups. Journal of Pure and Applied Algebra, 223 (6). pp. 2489-2529. doi:10.1016/j.jpaa.2018.09.004

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Official URL: https://doi.org/10.1016/j.jpaa.2018.09.004

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Abstract

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 -irreducible connected reductive subgroups for each simple classical factor of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type 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: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Linear algebraic groups, Representations of groups, Group theory
Journal or Publication Title: Journal of Pure and Applied Algebra
Publisher: Elsevier Science BV
ISSN: 0022-4049
Official Date: June 2019
Dates:
DateEvent
June 2019Published
13 September 2018Accepted
Volume: 223
Number: 6
Page Range: pp. 2489-2529
DOI: 10.1016/j.jpaa.2018.09.004
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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