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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
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: |
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| 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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