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Matrix Products and the Explicit 3, 6, 9, and 12-j Coefficients of the Regular Representation of SU(n)

Matrix Products and the Explicit 3, 6, 9, and 12-j Coefficients of the Regular Representation of SU(n),10.1063/1.1705141,L. M. Kaplan,M. Resnikoff

Matrix Products and the Explicit 3, 6, 9, and 12-j Coefficients of the Regular Representation of SU(n)  
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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.
Published in 1967.
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