Biorthogonal coupling coefficients of uq(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-recoupling (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.