Classification of some vertex operator algebras of rank 3
Classification of some vertex operator algebras of rank 3
复制标题
一些3阶顶点算子代数的分类
DOI：
10.2140/ant.2020.14.1613
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
G. Mason
中科院分区：
文献类型：
--
作者：
C. Franc;G. Mason
讨论了具有三个简单模的强正则顶点算子代数（VOAs）的分类，这些简单模的特征向量满足不可约一元一元一元一元线性微分方程。我们的主要定理以一个无限的仿射voa族、一个单独的仿射代数和两个Virasoro代数的形式提供了所有这些voa的分类，以及一个由11个例外字符向量组成的族和我们称之为$U$-系列的相关数据。我们证明了在Schellekens表全纯VOA中，至少有15个以交换子形式出现的$ $ VOA。其中包括仿射代数$E_{8,2}$和Hohn's Baby Monster VOA $\mathbf{VB}^\natural_{(0)}$，但其他$13$似乎是新的。证明主定理的思想是利用一组以有理函数为傅里叶系数的向量值模形式的性质，用广义超几何级数求解一组模线性微分方程。
We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy. Our Main Theorem provides a classification of all such VOAs in the form of one infinite family of affine VOAs, one individual affine algebra and two Virasoro algebras, together with a family of eleven exceptional character vectors and associated data that we call the $U$-series. We prove that there are at least $15$ VOAs in the $U$-series occurring as commutants in a Schellekens list holomorphic VOA. These include the affine algebra $E_{8,2}$ and Hohn's Baby Monster VOA $\mathbf{VB}^\natural_{(0)}$ but the other $13$ seem to be new. The idea in the proof of our Main Theorem is to exploit properties of a family of vector-valued modular forms with rational functions as Fourier coefficients, which solves a family of modular linear differential equations in terms of generalized hypergeometric series.