Irreducible A1 subgroups of exceptional algebraic groups

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 A(1) subgroups of exceptional algebraic groups G. Consequences are given concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible A(1) subgroups are determined by their composition factors on the adjoint module of G. (C) 2015 Elsevier Inc. All rights reserved.