su(3)k fusion coefficients

TL;DR

This paper presents a new diagrammatic method to derive explicit formulas for all su(3)_k fusion coefficients, simplifying the calculation of tensor product coefficients in the limit of large k.

Contribution

The paper introduces a novel diagrammatic approach that directly computes both tensor product and fusion coefficients for su(3)_k, providing explicit formulas applicable at finite and infinite levels.

Findings

Explicit formula for all su(3)_k fusion coefficients

Simplified expression for su(3) tensor product coefficients as k approaches infinity

New diagrammatic method for computing fusion and tensor product coefficients

Abstract

A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is presented which, in the limit $k \rightarrow \infty$, turns into a simple and compact expression for the $su(3)$ tensor product coefficients. The derivation is based on a new diagrammatic method which gives directly both tensor product and fusion coefficients.