Simple Irreducible Subgroups of Exceptional Algebraic Groups

Abstract

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible subgroups of exceptional algebraic groups $G$ which are connected, closed and simple of rank at least $2$. Consequences are given concerning the representations of such subgroups on various $G$-modules: for example, with one exception, the conjugacy classes of irreducible simple connected subgroups of rank at least $2$ are determined by their composition factors on the adjoint module for $G$.

46 pages; version to appear in J. Alg

References in corpus (2)

• Irreducible A_1 Subgroups of Exceptional Algebraic Groups
• Complete Reducibility in Euclidean Twin Buildings

Cited by in corpus (6)

• Irreducible A_1 Subgroups of Exceptional Algebraic Groups
• On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
• Non-separability and complete reducibility: $E_n$ examples with an application to a question of Külshammer
• On the smoothness of normalisers and the subalgebra structure of modular Lie algebras
• A New Maximal Subgroup of $E_8$ in Characteristic $3$
• Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields 2