BIORTHOGONAL COUPLING-COEFFICIENTS OF U(Q)(N)

The coupling (Wigner-Clebsch-Gordan) coefficients and their isofactors for the unitary quantum algebras u(q)(n) with the repeating irreducible representations in the coproduct decomposition are considered. Generalizing the U(n) case, the biorthogonal systems of the u(q)(n) isofactors with the dual multiplicity labels are constructed by means of the recoupling technique in terms of the isofactors with simpler multiplicity structure. A first construction, correlated with the inverted Littlewood-Richardson rules, gives the bilinear combinations of isofactors after applying the proportionality of the q-recoupiing (Racah) coefficients to the boundary q-isofactors. An alternative recursive construction gives the nonorthogonal q-isofactors satisfying the most elementary boundary conditions and proportional to the u(q)(n-1) recoupling coefficients for some less restricted values of parameters. Some multiplicity-free and more general u(q)(n) recoupling coefficients are found, the blocks (bilinear combinations) of which (equal to the resubducing coefficients of the complementary chains of q-algebras) are proposed to use for the orthonormalization of some u(q)(n) biorthogonal isofactors, including the general u(q)(3) case.