abstract: Let G be a simple algebraic group of rank at least 2 defined over an algebraically closed field of characteristic 0 and let f be an irreducible representation of G whose image lies in SL(V), Sp(V) or SO(V). We consider two closely related problems, first the problem of determining those representations for which distinguished unipotent elements of G are sent to distinguished elements of the classical group on V. Also we settle a base case of the general problem of determining when the restriction of f to a simple subgroup of G is multiplicity-free. This is joint work with Martin Liebeck and Gary Seitz