Coupling coefficients for the irreducible representations of the space group of garnet

Abstract

We have computed the Clebsch-Gordan coefficients of the representations for the space group O 10 h(Ia3d) of the garnet structure. We enumerate all arms of the wave vector stars and all wave vector selection rules. As an example we compute the matrices of the Clebsch-Gordan coefficients for the decomposition of Kronecker squares of the irreducible representations at one symmetry point, N, on the surface of the first Brillouin zone into irreducible representations at the zone centre, Λ.