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In this paper we present the generating function method for the derivation ofbosons polynomials of Gel'fand basis and Wigner coefficients for the canonicalbasis of SU(n). We find a new analytic polynomial basis of SU(4) with the exactnumber of summations, five only. We find also a new algebraic expression ofWigner coefficient with multiplicity for the canonical basis and the isoscalorsfactors of SU (3) with only. three summations.

The "boson polynomials" of Gel'fand basis and the analytic expression of  Wigner's coefficients with multiplicity for the canonical basis of unitary  groups