Quantum dimensions and fusion rules for parafermion vertex operator algebras

TL;DR

This paper determines the quantum dimensions and fusion rules for parafermion vertex operator algebras linked to affine Kac-Moody algebra A_1^{(1)} at level k, advancing understanding of their algebraic structure.

Contribution

It provides explicit calculations of quantum dimensions and fusion rules for a class of parafermion vertex operator algebras, a novel contribution in the field.

Findings

Quantum dimensions are explicitly calculated.

Fusion rules for the parafermion vertex operator algebra are established.

Results apply to the affine Kac-Moody algebra A_1^{(1)} at arbitrary level k.

Abstract

The quantum dimensions and the fusion rules for the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of level k are determined.