Representations and fusion rules for the orbifold vertex operator algebras $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$

Abstract

For the cyclic group ${\mathbb{Z}}_3$ and positive integer $k$, we study the representations of the orbifold vertex operator algebra $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$. All the irreducible modules for $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$ are classified and constructed explicitly. Quantum dimensions and fusion rules for the orbifold vertex operator algebra $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$ are completely determined.

27 pages

References in corpus (1)

• Fusion rules for ${\mathbb{Z}}_2$-orbifolds of affine and parafermion vertex operator algebras