Irreducible disconnected subgroups of exceptional algebraic groups

Abstract

This paper studies the irreducible embeddings of simple algebraic groups of exceptional type. It is motivated by the role of such embeddings in the study of positive dimensional closed subgroups of classical algebraic groups. In this paper we give a classification of all triples ( G , Y , V ) where Y is a simple algebraic group of exceptional type, defined over an algebraically closed field K of characteristic p > 0 , G is a closed disconnected positive dimensional subgroup of Y and V is a nontrivial rational irreducible KY -module on which G acts irreducibly.