MULTIPLICITY-FREE U(Q)(N) COUPLING-COEFFICIENTS

The coupling (Wigner-Clebsch-Gordan) coefficients of the unitary quantum algebras u(q)(n) are considered. The tensorial properties of the generator powers and their ordered products, used in the explicit projectors and weight lowering procedures, are established. Different expressions for the multiplicity-free isofactors of u(q)(n) coupling coefficients (those coupling an arbitrary and symmetric representations) are derived. Explicit expression of the arbitrary isofactors in terms of their boundary values are proposed. Proportionality of the semistretched isofactors to the stretched q-recoupling coefficients of u(q)n - 1) (q-analogures of 9 j-symbols) is demonstrated. The stretched isofactors of u(q)(3) are expressed in terms of Clebsch-Gordan coefficients of u(q)(2).