On some properties of SU(3) Fusion Coefficients

TL;DR

This paper explores properties of SU(3) fusion coefficients, providing explicit generating polynomials, deriving new identities, and extending conjugation properties from classical to affine algebra at finite level.

Contribution

It introduces explicit generating polynomials, generalizes classical identities, and extends conjugation properties to affine SU(3) fusion coefficients.

Findings

Explicit generating polynomials for fusion coefficients

New identities generalizing Freudenthal-de Vries formula

Extended conjugation properties to affine algebra at finite level

Abstract

Three aspects of the SU(3) fusion coefficients are revisited: the generating polynomials of fusion coefficients are written explicitly; some curious identities generalizing the classical Freudenthal-de Vries formula are derived; and the properties of the fusion coefficients under conjugation of one of the factors, previously analysed in the classical case, are extended to the affine algebra of su(3) at finite level.