Space group Clebsch-Gordan coefficients. I. Special solutions of the multiplicity problem and Dirl's criterion
Brian Davies · Journal of Physics A Mathematical and General · 1986
The wavevector selection rules (WVSR) occurring in the reduction of Kronecker products of space group unirreps are classified, for convenience, into three types. For WVSR of type I, Dirl (1979) has shown that special solutions of the multiplicity problem always exist. For WVSR of type II, Dirl has given a simple criterion for the existence for special solutions of the multiplicity problem and the authors show that, for all 230 (single and double) space groups, the Miller and Love matrix unirreps satisfy this criterion. WVSR of type III will be considered in a subsequent paper.