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

TL;DR

This paper introduces a generating function approach to derive boson polynomials of Gel'fand basis and Wigner coefficients for SU(n), presenting new analytic polynomial bases and simplified algebraic expressions with fewer summations.

Contribution

It provides a novel generating function method for deriving boson polynomials and Wigner coefficients, including new polynomial bases and simplified algebraic expressions for SU(4) and SU(3).

Findings

New analytic polynomial basis of SU(4) with five summations

Algebraic expression of Wigner coefficient with three summations

Simplified formulas for isoscalars factors of SU(3)

Abstract

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