Matrix Products and the Explicit 3, 6, 9, and 12j Coefficients of the Regular Representation of SU(n)
Abstract
The explicit Wigner coefficients are determined for the direct product of regular representations, (N)⊗(N)=2(N)+…, of SU(n), where N = n^{2}  1. Triple products C_{m}C_{i}C_{m} = αF_{i} + βD_{i}, and higherorder products, are calculated, where C_{i} may be F_{i} or D_{i}, the N × N Hermitian matrices of the regular representation, and m is summed. The coefficients α, β are shown to be 6j symbols, and higherorder products yield the explicit 9j, 12j, symbols. A theorem concerning (3p)j coefficients is proved.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 November 1967
 DOI:
 10.1063/1.1705141
 Bibcode:
 1967JMP.....8.2194K