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Complete reducibility in good characteristic
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Litterick, Alastair J. and Thomas, Adam (2018) Complete reducibility in good characteristic. Transactions of the American Mathematical Society, 370 . pp. 5279-5340. doi:10.1090/tran/7085
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Official URL: https://doi.org/10.1090/tran/7085
Abstract
Let $ G$ be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic $ p \ge 0$. 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 subgroup of $ P$. In this paper we determine the $ G$-conjugacy classes of non-$ G$-cr simple connected subgroups of $ G$ when $ p$ is good for $ G$. For each such subgroup $ X$, we determine the action of $ X$ on the adjoint module $ L(G)$ and the connected centraliser of $ X$ in $ G$. As a consequence we classify all non-$ G$-cr connected reductive subgroups of $ G$, and determine their connected centralisers. We also classify the subgroups of $ G$ which are maximal among connected reductive subgroups, but not maximal among all connected subgroups.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Representations of groups, Homology theory | ||||||
| Journal or Publication Title: | Transactions of the American Mathematical Society | ||||||
| Publisher: | American Mathematical Society | ||||||
| ISSN: | 0002-9947 | ||||||
| Official Date: | 17 April 2018 | ||||||
| Dates: |
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| Volume: | 370 | ||||||
| Page Range: | pp. 5279-5340 | ||||||
| DOI: | 10.1090/tran/7085 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Publisher Statement: | “First published in Transactions of the American Mathematical Society in 370, 2018, published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | © Copyright 2018 American Mathematical Society | ||||||
| RIOXX Funder/Project Grant: |
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