Let $V$ be a strongly regular vertex operator algebra and let $\mathfrak{ch}_V$ be the space spanned by the characters of the irreducible $V$-modules. It is known that $\mathfrak{ch}_V$ is the space of solutions of a so-called modular linear differential equation (MLDE). In this paper we obtain a classification of those $V$ for which the corresponding MLDE is irreducible and monic of order $2$. It turns out that $V$ is either one of seven affine Kac–Moody algebras of level $1$, or the Yang–Lee Virasoro VOA of central charge $c = - 22/5$. Our proof establishes new connections between the characters of $V$ and Gauss hypergeometric series, and as a Corollary of our classification we complete the work of Mathur, Mukhi and Sen who considered a closely related problem thirty years ago.

中文翻译：

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等级为$ 2 $的顶点算子代数：重新讨论了Mathur–Mukhi–Sen定理

假设$ V $是一个强规则的顶点算子代数，并且让$ \ mathfrak {ch} _V $是不可约的$ V $-模块的字符所跨越的空间。已知$ \ mathfrak {ch} _V $是所谓的模块化线性微分方程（MLDE）的解的空间。在本文中，我们获得了这些$ V $的分类，对应的MLDE是不可约的，其单价为$ 2 $。事实证明，$ V $是七个$ 1 $仿射Kac-Moody代数之一，或者是中心电荷$ c =-22/5 $的Yang-Lee Virasoro VOA。我们的证明在$ V $的字符和高斯超几何序列之间建立了新的联系，作为我们分类的推论，我们完成了Mathur，Mukhi和Sen的工作，他们三十年前曾考虑过一个密切相关的问题。