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Multiplicity-free Representations of Algebraic Groups Noemi Fernandez Selva sociologist Tim Delaney looks atLet K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V), where H is a proper connected subgroup of G, and V is a finite dimensional irreducible G module such that the restriction of V to H is multiplicity free that is, each of its composition factors appears with multiplicity 1. A great deal of classical work, going back to Dynkin,