Litterick, Alastair J and Thomas, Adam R (2019) Reducible subgroups of exceptional algebraic groups. Journal of Pure and Applied Algebra, 223 (6). pp. 2489-2529. DOI https://doi.org/10.1016/j.jpaa.2018.09.004
Litterick, Alastair J and Thomas, Adam R (2019) Reducible subgroups of exceptional algebraic groups. Journal of Pure and Applied Algebra, 223 (6). pp. 2489-2529. DOI https://doi.org/10.1016/j.jpaa.2018.09.004
Litterick, Alastair J and Thomas, Adam R (2019) Reducible subgroups of exceptional algebraic groups. Journal of Pure and Applied Algebra, 223 (6). pp. 2489-2529. DOI 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 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 |
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Additional Information: | Comments: 47 pages. Final version, to appear in Journal of Pure and Applied Algebra. Minor changes with respect to previous version |
Uncontrolled Keywords: | math.GR; math.RT; 20G07, 20G41 (Primary), 20G10 (Secondary) |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 05 Sep 2019 09:44 |
Last Modified: | 07 Aug 2024 19:56 |
URI: | http://repository.essex.ac.uk/id/eprint/25257 |
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Filename: 1801.09266v2.pdf
Licence: Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0