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.

中文翻译：

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双峰顶点算子代数L sl 2 ̂（k，0）Z p的表示和融合规则

摘要

对于循环群 ${\mathbb{ž}}_p$（p是素数）和一个正整数k，我们研究球面顶点算子代数的表示${\mathrm{大号}}_{\widehat{\mathfrak{s}{\mathfrak{升}}_2}}{（ķ，0）}^{{\mathbb{ž}}_p}$。所有不可约模块${\mathrm{大号}}_{\widehat{\mathfrak{s}{\mathfrak{升}}_2}}{（ķ，0）}^{{\mathbb{ž}}_p}$被明确分类和构造。量子尺寸和聚变规则${\mathrm{大号}}_{\widehat{\mathfrak{s}{\mathfrak{升}}_2}}{（ķ，0）}^{{\mathbb{ž}}_p}$ 完全确定。