Irreducible A_1 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 $A_1$ 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 $G$.

51 pages; published in J. Alg

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• Alternating Subgroups of Exceptional Groups of Lie Type
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