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A closed subgroup of a semisimple algebraic group is called irreducible if itlies in no proper parabolic subgroup. In this paper we classify all irreducible$A_1$ subgroups of exceptional algebraic groups $G$. Consequences are givenconcerning the representations of such subgroups on various $G$-modules: forexample, the conjugacy classes of irreducible $A_1$ subgroups are determined bytheir composition factors on the adjoint module of $G$.

Irreducible A_1 Subgroups of Exceptional Algebraic Groups