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A general procedure for the derivation of SU(3)\supset U(2) reduced Wignercoefficients for the coupling (\lambda_{1}\mu_{1})\times(\lambda_{2}\mu_{2})\downarrow (\lambda\mu)^{\eta}, where \eta is the outermultiplicity label needed in the decomposition, is proposed based on arecoupling approach according to the complementary group technique given in(I). It is proved that the non-multiplicity-free reduced Wigner coefficients ofSU(n) are not unique with respect to canonical outer multiplicity labels, andcan be transformed from one set of outer multiplicity labels to another. Thetransformation matrices are elements of SO(m), where m is the number ofoccurrence of the corresponding irrep (\lambda\mu) in the decomposition(\lambda_{1}\mu_{1})\times (\lambda_{2}\mu_{2})\downarrow (\lambda\mu). Thus, akind of the reduced Wigner coefficients with multiplicity is obtained after aspecial SO(m) transformation. New features of this kind of reduced Wignercoefficients and the differences from the reduced Wigner coefficients withother choice of the multiplicity label given previously are discussed. Themethod can also be applied to the derivation of general SU(n) Wigner or reducedWigner coefficients with multiplicity. Algebraic expression of another kind ofreduced Wigner coefficients, the so-called reduced auxiliary Wignercoefficients for SU(3)\supset U(2), are also obtained.Comment: 30 pages, LaTe

Complementary group resolution of the SU(n) outer multiplicity problem. II. Recoupling approach for SU(3)⊃U(2) reduced Wigner coefficients