Subgroups of exceptional algebraic groups which are irreducible on an adjoint or minimal module

Abstract

Let G be a simple algebraic group of exceptional type over an algebraically closed field K of characteristic p. The purpose of this paper is to determine all maximal closed subgroups of G which act irreducibly on either the adjoint G-module or one of the well-known “minimal” modules of dimension 56, 27, 26− δp,3 or 7− δp,2 for G of type E7, E6, F4 or G2 respectively. (The adjective “minimal” here refers to the minimality of the dimension.) This greatly extends [21, Theorem 4] for exceptional groups.