Applications of generating function method to the symmetry and the Kronecker products of SU(n) representations

Abstract

Using the generating function of SU(n) we find the conjugate state of SU(n) basis and we find in terms of Gel'fand basis of SU(3(n-1)) the representation of the invariants of the Kronecker products of SU(n). We find a formula for the number of the elementary invariants of SU(n). We apply our method to the coupling of SU(3) and we find a new expression of the isoscalar of Wigner symbols ($\lambda 10,\lambda 2 \mu 2; \lambda 3 \mu 3$).