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Complete reducibility in good characteristic

Litterick, Alastair J and Thomas, Adam R (2018) 'Complete reducibility in good characteristic.' Transactions of the American Mathematical Society, 370 (8). 5279 - 5340. ISSN 0002-9947

1505.00939v2.pdf - Accepted Version

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Let G be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic p ≥ 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: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 04 Sep 2019 14:47
Last Modified: 04 Sep 2019 15:15

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