Complete reducibility in good characteristic

Alastair Litterick, Adam R Thomas

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)
264 Downloads (Pure)

Abstract

Let G be a simple algebraic group of exceptional type, over analgebraically closed field of characteristic p0. A closed subgroup H of G is called G-completely reducible (G-cr) if whenever H is containedin 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 simpleconnected 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 theconnected 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 amongconnected reductive subgroups, but not maximal among all connected subgroups.
Original languageEnglish
Pages (from-to)5279-5340
Number of pages62
JournalTransactions of the American Mathematical Society
Volume370
Early online date17 Apr 2018
DOIs
Publication statusE-pub ahead of print - 17 Apr 2018

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