Determination of the Weyl invariants and calculation of the coupling coefficients for unitary groups

The author presents a new approach for determining the Weyl invariants of unitary groups. Such an approach is based on the generating function of the basis of the representation for unitary groups built in an earlier work (Hage Hassan 1983). The author obtains two expressions for the Weyl invariants, both including the parameters involved in the generating function. Coupling coefficients appear in one of the expressions. The comparison of the development of the two expressions allows the calculation of the coupling coefficients. The application of this approach to the calculation of the coupling coefficients for the direct product ( lambda 1 0)(X)( lambda 2 mu 2 ) of SU(3) leads to an expression of the isoscalar factor where no summation occurs in contradistinction with the known expression for the coupling coefficients which involve five summations.