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A general yet simple and hence practical algorithm for calculating SU 3 ⊃ SU2 × U1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by-product of the initial steps in the SU3 ⊃ SU2 × U1 Wigner coefficient construction algorithm. A general expression for evaluating SU3 ⊃ R3 Wigner coefficients as a sum over a simple subset of the corresponding SU3 ⊃ SU2 × U1 Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SU3 ⊃ SU2 × U1 and SU3 ⊃ R3 Wigner coefficients are given. Machine codes based on the results are available. ©1973 by the American Institute of Physics.

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Journal of Mathematical Physics

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