WEYL Q-COEFFICIENTS FOR U(Q)(3) AND RACAH Q-COEFFICIENTS FOR SU(Q)(2)

With the aid of the projection-operator technique, the general analyti c expression for the elements of the matrix that relates the U and T b ases of an arbitrary finite-dimensional irreducible representation of the u(q)(3) quantum algebra (Weyl q-coefficients) is obtained for the case where the deformation parameter q is not equal to a square root o f unity. The procedure for resummation of q-factorial expressions is u sed to prove that, module phase factors, these Weyl q-coefficients coi ncide with Racah q-coefficients for the su(q)(2) quantum algebra. It i s also shown that, on the basis of one general formula, the q-analogs of all known general analytic expressions for the 6j symbols (and Raca h coefficients) of the Lie algebras of the angular momentum can be obt ained by using this resummation procedure. The symmetry properties of these q coefficients are discussed. The result is formulated in the fo llowing way: the general formulas for the q-6j symbols (Racah q-coeffi cients) of the su(q)(2) quantum algebra are obtained from the general formulas for the conventional 6j symbols (Racah coefficients) of the s u(2) Lie algebra by replacing directly all factorials with q-factorial s, the symmetry properties of the q-6j symbols being completely coinci dent with the symmetry properties of the conventional 6j symbols.