A new perspective on the Frenkel-Zhu fusion rule theorem

TL;DR

This paper proves a formula for fusion coefficients in affine Kac-Moody algebras, generalizing classical tensor product theorems and confirming a conjecture by Walton.

Contribution

It provides a new formula for fusion coefficients, offering a reformulation of the Frenkel-Zhu fusion rule theorem as a broad generalization of classical tensor product results.

Findings

Proved a formula for fusion coefficients in affine Kac-Moody algebras.

Reformulated the Frenkel-Zhu fusion rule theorem.

Connected fusion rules to classical tensor product theorems.

Abstract

In this paper we prove a formula for fusion coefficients of affine Kac-Moody algebras first conjectured by Walton [Wal2], and rediscovered in [Fe]. It is a reformulation of the Frenkel-Zhu affine fusion rule theorem [FZ], written so that it can be seen as a beautiful generalization of the classical Parasarathy-Ranga Rao-Varadarajan tensor product theorem [PRV].