Representations of the orbifold VOAS $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^K$ and the commutant VOAS $C_{{L_{\widehat{{\mathfrak{so}}_m}}(1,0)}^{\otimes 3}}(L_{\widehat{{\mathfrak{so}}_m}}(3,0))$

Abstract

For the Klein group $K$, $k\in {\mathbb{Z}}_{⩾1}$ and $m\in {\mathbb{Z}}_{⩾4}$, we study the representations of the orbifold vertex operator algebra $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^K$ and the commutant vertex operator algebra of $L_{\widehat{{\mathfrak{so}}_m}}(3,0)$ in $L_{\widehat{{\mathfrak{so}}_m}}(1,0{)}^{\otimes 3}$ which can be realized as the orbifold vertex operator subalgebra $L_{\widehat{{\mathfrak{sl}}_2}}(2m,0{)}^K$ or its extension. All the irreducible modules for $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^K$ and $C_{{L_{\widehat{{\mathfrak{so}}_m}}(1,0)}^{\otimes 3}}(L_{\widehat{{\mathfrak{so}}_m}}(3,0))$ are classified and constructed explicitly.

A typo corrected on page $11$: $-$ in the equation (4.3) should be $+$

References in corpus (2)

• Tensor Decomposition, Parafermions, Level-Rank Duality, and Reciprocity Law for Vertex Operator Algebras
• Fusion rules for ${\mathbb{Z}}_2$-orbifolds of affine and parafermion vertex operator algebras

Cited by in corpus (1)

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