The representation groups and projective representations of the point groups and their applications

Abstract

The different representation groups of the point groups are established and their character tables presented. These enable one to construct equivalent alternative sets of projective representations, as well as to provide an easy route to the determination of double group and space group representations. It is shown that these are uniquely determined, independent of the choice of representation group, but the availability of alternative representation groups allows greater scope for the processes of ascent and descent in symmetry, which are quite restricted in the context of projective representations.