Space Group Selection Rules: Diamond and Zinc Blende

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Abstract
General methods for the reduction of direct products of space-group irreducible representations are discussed, based on the use of full irreducible representations of the space group. The reduction proceeds in two stages: First, wave vector selection rules are obtained when the direct product of two stars is decomposed into a direct sum of stars; finally, the species of irreducible representations occurring for each star in the sum is found. The latter stage is accomplished by using the "reduction group," or by "direct inspection," depending on convenience. These methods can be applied to the reduction of the ordinary Kronecker products, and the symmetrized Kronecker powers, of the full space group irreducible representations of any space group.

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