Representations and fusion rules for the orbifold vertex operator algebras Lsl2̂(k,0)Zp

Abstract

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

Keywords:

• Orbifold vertex operator algebras
• irreducible modules
• quantum dimensions
• fusion rules

2010 Mathematics Subject Classification:

• 17B69

Acknowledgement

The author thanks the referee for carefully reading the article and for invaluable comments and suggestions.

Additional information

Funding

This study was supported by China NSF grant No.11771281 and SNSFC grant No.16ZR1417800.