Generating function of isoscalar factors of unitary groups

Abstract

The author introduces a new schematisation of the elements of the bases of the fundamental representations of the unitary groups. Using this schematisation, as well as two rules which will be established in this work, the author is able to find, by an elementary calculation, the generating function of coupling coefficients of this basis. This last generating function permits the author to find the one corresponding to SU(n) isoscalar factors. The approach gives in the general case, i.e. for every n, the algebraic expressions of these factors. The author shows that to find the elements of the irreducible representation of the direct product of N representations, and gives the details of this method in the special case n=2. A priori, the method can be easily applied to other classical groups.