Vector coherent state constructions of U(3) symmetric tensors and their SU(3)⊇SU(2)×U(1) Wigner coefficients

Generalized vector coherent state constructions of totally symmetric U(3) tensors are used to gain new expressions for the SU(3)⊇SU(2)×U(1) Wigner coefficients for the coupling (λ1μ1)×(λ20)→(λ3μ3). These expressions show how the extremely simple formulas of Le Blanc and Biedenharn, involving a single 9-j coefficient, arise as special cases of a general result that involves 12-j coefficients. A simpler general result involving only 9-j coefficients and K-normalization factors is derived in a way that can, in principle, be generalized to the generic coupling with multiplicity.