Non-monomial multiplier representations of abelian groups (Q1175012)

It is known that if \(\sigma\) is a type I multiplier of a locally compact nilpotent group \(G\) then every irreducible \(\sigma\)-representation of \(G\) is induced by a one dimensional \(\sigma\)-representation of a closed subgroup of \(G\). Under the additional conditions that \(G\) is abelian and discrete, the converse of this was proved by two of the authors (A. L. Carey and W. Moran). It is shown in this paper that the converse is true if \(G\) is merely abelian and not necessarily discrete.