Universal overgroup

A way to separate irreducible unitary representations ππ for a Lie group GG by moment sets is to use an infinite-dimensional overgroup G˜ and extensions of each representation ππ to a representation π˜ of G˜, in such a manner that the moment set of π˜ characterizes ππ.In this paper we propose a universal overgroup G˜, which is an infinite-dimensional Fréchet–Lie group. We extend each ππ to a Hamiltonian action π˜ of G˜. The moment set of π˜ characterizes ππ.