Generating function of unitary group isoscalar factors

In this paper we introduce a new schematization of the elements of the unitary group fundamental representation basis. Using this schematization as well as two rules which will be establish in this work, we was able to find by an elementary calculus, the generating function of the Gel'fand basis of unitary group, and the generating function of coupling coefficients. This last generating function permits us to find the one corresponding to SU(n) isoscalar factors. Our approach is the only one which give in the general case, i.e. for every n, an explicit expression of these factors. We show how to find the elements of the irreducible representation of the direct product of N representations, and we give the details of this method in the special case n = 2. A priori, our method can be easily applied to other classical groups