Multiplicity-free subgroups of reductive algebraic groups

We introduce the notion of a multiplicity-free subgroup of a reductive algebraic group in arbitrary characteristic. This concept already exists in the work of Kramer for compact connected Lie groups. We give a classification of reductive multiplicity-free subgroups, and as a consequence obtain a simple proof of a theorem of Kleshchev. (C) 1997 Academic Press.