Abstract
Reduction of SU 2 with respect to the double cover of the octahedral group shows how spin is realized on a cubic lattice. Only spins 0, 1 2 , 1 and 3 2 are described by single octahedral irreducible representations; higher spins are described by two or more. The reduction procedure is accompanied by useful methods for constructing octahedral wave functions. Remarks on angular momentum assignments in lattice dynamical calculations are illustrated by a simple soluble model.
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