Reduction of Kronecker Products of Space Group Representations in the Frame-Work of Little Group Theory

摘要

A general method for the reduction of the representions of space groups is discussed, making use of their allowable representations. Given any representation this method depends on finding some appropriate representations of suitable groups of wave vectors of the space group which are then decomposed into different allowable representations of them. As the irreducible representations of the space group are uniquely defined by its allowable representations, by this procedure the complete reduction of the given representation is effected. This method is first applied, for orientation to the analysis of reality condition and compatibility relations of space group irreducible representations and the symmetry modes of vibrations of crystals. Then it is extended to the reduction of the Kronecker products, both ordinary and symmetric, of the irreducible representations of space groups. As the final reduction is accomplished with respect to the groups of wave vectors this method fits in the frame work of the little group technique. (Author)