On the projective representations of finite Abelian groups. II

Abstract

Complete sets of inequivalent irreducible projective representations of Cnm ={w1,⋅⋅⋅,wn; wmi =1, i=1,...,n; wiwj =wjwi, i, j=1,...,n} with respect to a class of factor sets α are determined, where α(wi,wj) =θα(wj,wi), 1≤i<j≤n and θ is a fixed mth root of unity. A single irreducible projective representation of Cnm for each factor set α is constructed and called the basic projective representation. The rest of the representations are obtained by tensoring the basic projective representations with some ordinary representations of Cnm. Projective representations of Cnm are thus parametrized in terms of its ordinary representations.