Multiplicity-free super vector spaces

Abstract: We consider semisimple Lie groups over C acting on a super vectorspace V = V_0 + V_1 such that the supersymmetric algebra P(V) = S(V_0) \otimes \Lambda(V_1) decomposes multiplicity-free. Such spaces are of particular interest in invariant theory. If V = V_1 the action is called skew multiplicity-free (skew MF). By discussing some examples of skew MF modules we explain a necessary condition on V = V_1 to be skew MF. Furthermore, we show how this can be generalized to a condition on arbitrary multiplicity-free superspaces and give a classifcation result.