Mackey's criterion for subgroup restriction of Kronecker products and harmonic analysis on Clifford groups

We present a criterion for multiplicity-freeness of the decomposition of the restriction of the Kronecker product of two irreducible representations of a finite group G with respect to a subgroup H≤G. This constitutes a generalization of a well known criterion due to Mackey (which corresponds to the case H=G). The corresponding harmonic analysis is illustated by detailed computations on the Clifford groups.