Projective representations of abelian groups

Abstract:

Let $\omega$ be a factor system for the locally compact abelian group G. Then we show that the finite-dimensional unitary irreducible projective representations of G, having factor system $\omega$, possess a common dimension $d(\omega )$. Using a characterisation of $d(\omega )$ as the index in G of a maximal subgroup on which $\omega$ is symmetric we derive a formula for $d(\omega )$ in the case that G is discrete and finitely generated.