Some comments on the theory of space-group representations. II. Basic domain and representation domain

Abstract

For pt. I see ibid., vol. 3, no.3, 610 (1970). Tables of space-group representations now available are incomplete for those space groups which do not have the full symmetry of the Bravais lattice on which they are based. It is shown that this defect can be overcome without recourse to further tabulation for all space groups except Pa3(T_h⁶). This particular space group is considered separately, and is shown to be exceptional in that alone out of all the 230 space groups it possesses two k-vectors, which are related by an operation of the holosymmetric point group, but whose groups of k possess small representations of different dimensionalities. Nor does the addition of time reversal remove this anomaly.