Ray representations of point groups and the irreducible representations of space groups and double space groups

Abstract

The theory of the ray representations of a finite group is summarized and full matrix ray representations are derived and tabulated for all thirty-two point groups. It is shown that any irreducible representation of any of the 230 space groups and of the corresponding double groups may be obtained quickly and easily from these ray representations of the point groups. The most complex cases which arise, namely points of high symmetry on the surface of the Brillouin zone for the regular holohedric space groups, 01 ... OJ°, are treated explicitly. The relation of the present work to the recent treatments of Slater and Kovalev is discussed.