Twisted actions and the obstruction to extending unitary representations of subgroups

الأصل · EN

Suppose that G is a locally compact group and π is a (not necessarily irreducible) unitary representation of a closed normal subgroup N of G on a Hilbert space H. We extend results of Clifford and Mackey to determine when π extends to a unitary representation of G on the same space H in terms of a cohomological obstruction.