Kronecker products of projective representations of translation groups

Irreducible projective representations of the translation group of a finite N x N two-dimensional lattice can be labeled by symbols (n,l; q), where N = vn, gcd(l, n) = 1 and q denotes an irreducible representation of Z(v)(2). The Kronecker product of such representations can be decomposed into irreducible ones but, in general, with a factor system different from factor systems of coupled representations. It corresponds to changes in the magnetic period and is caused by addition of charges of interacting particles.