Classification of irreducible highest weight modules for the parafermion vertex algebras $N_k({\mathfrak{sl}}_2)$ at arbitrary level

Drazen Adamovic, Qing Wang

Let $N^k({\mathfrak{sl}}_2)$ be the universal parafermion vertex algebra and $N_k({\mathfrak{sl}}_2)$ its simple quotient. We classify all irreducible highest weight $N^k(\mathfrak{sl}…