Induced projective representations

The left- (right-) regular projective representation of a finite group G and the corresponding ’’projective’’ representation of the left-group algebra are defined for a given standard factor system, and special features of these constructions are discussed. Starting from a given projective unitary irreducible representation of a normal (but not necessarily Abelian) subgroup N of G, we obtain by induction the matrix elements of the projective unitary irreducible representations of G, where the corresponding group algebra is used as aid. These considerations are of interest for the construction of projective unitary irreducible representations of little cogroups of nonsymmorphic space groups. For the present method allows us to construct, for a q lying on the ’’surface’’ of the Brillouin zone, these projective representations out from unitary irreducible representations belonging to q’s of ’’lower’’ symmetry. This method is used to determine for all little cogroups of the nonsymmorphic space group Pn3n complete sets of projective unitary irreducible representations.