Projective Representations of Abelian Groups

Let G be a finite elementary abelian p-group. Given a 2-cocycle α of G over the field of complex numbers, we show how to construct an irreducible projective representation of G with 2-cocycle in the cohomology class of α. Let S be a subgroup of G of index dividing p2. Then we also count (in each possible case) the number of cohomology classes in the Schur multiplier of G, whose corresponding irreducible projective representations behave the same upon restriction to S.