Characters of $\hat{sl}(4)_k$ fusion algebra at non-rational level

TL;DR

This paper constructs the fusion ring of a quasi-rational $ ext{sl}(4)_k$ WZNW theory at generic levels, extending the formal characters of finite-dimensional representations using the affine Weyl group.

Contribution

It introduces a novel construction of the fusion ring for $ ext{sl}(4)_k$ at non-rational levels using the affine Weyl group and formal characters.

Findings

Fusion ring generated by elements in the group ring of the affine Weyl group.

Extension of formal characters of finite-dimensional $ ext{sl}(4)$ representations.

Applicable at generic, non-rational levels $k$.

Abstract

We construct the fusion ring of a quasi-rational $\hat{sl}(4)_k$ WZNW theory at generic level $k \not\in Q$. It is generated by commutative elements in the group ring $Z[\tilde{W}]$ of the affine Weyl group $\tilde{W}$ which extend polynomially the formal characters of finite dimensional representations of $sl(4)$.