Matrix Products and the Explicit 3, 6, 9, and 12-j Coefficients of the Regular Representation of SU(n)
The explicit Wigner coefficients are determined for the direct product of regular representations, (N)⊗(N)=2(N)+…, of SU(n), where N = n2 - 1. Triple products CmCiCm = αFi + βDi, and higher-order products, are calculated, where Ci may be Fi or Di, the N × N Hermitian matrices of the regular representation, and m is summed. The coefficients α, β are shown to be 6-j symbols, and higher-order products yield the explicit 9-j, 12-j, symbols. A theorem concerning (3p)-j coefficients is proved.