On Projective Unitary-Antiunitary Representations of Finite Groups

Abstract

A generalization of Schur's treatment of projective representations is discussed for a very general class of representations occurring in physical theories: the projective representations by unitary and antiunitary operators. It is shown that for every finite group the projective unitary-antiunitary (PUA) representations can be obtained from the ordinary unitary-antiunitary representations of another finite group. The construction of such a representation group is treated. As an example we apply the theory for the determination of irreducible representations of subgroups of the Poincaré group. The classes of PUA representations for all finite crystallographic groups in spaces of dimension up to four are explicitly given.