Complete reducibility in good characteristic

Alastair J. Litterick, Adam R. Thomas
2018 Transactions of the American Mathematical Society  
General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: Abstract 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
more » ... is 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.
doi:10.1090/tran/7085 fatcat:yvylvmsh6bdxfjdwctyz4k3ly4