AI 中文总结
该研究针对有理共形场论特征标求解模线性微分方程难题，引入微分算子，将高$\ell$值解与低$\ell$值解联系，保持相关性质，简化高$\ell$拟特征标构造，为组织候选特征标提供新途径，并应用于证明关于$\ell = 2$拟特征标符号的猜想。
AI 中文摘要
有理共形场论的特征标可解由其阶数和朗斯基行列式指标$\ell$标记的模线性微分方程。在较高的$\ell$值时，通过求解模线性微分方程对允许解进行直接分类变得越来越困难，此时会出现可移动极点和辅助参数。在这项工作中，我们引入了微分算子，这些算子将较高$\ell$值的解与较低$\ell$值的解联系起来，同时保持模协变性和$q$级数的整数性。在秩为二时，这从马图尔 - 穆克希 - 森方程生成了所有允许的朗斯基行列式扇区。在秩为三及更高时，它将较高$\ell$值的拟特征标的构造简化为具有较低$\ell$值的更简单方程。这为在朗斯基行列式塔中组织候选有理共形场论特征标以及更一般的拟特征标提供了一条有效的新途径。作为应用，我们应用我们的构造证明了关于秩为二时$\ell = 2$拟特征标符号的一个先前猜想的性质。
英文摘要
Characters of rational conformal field theories solve modular linear differential equations labelled by their order and the Wronskian index $\ell$. Direct classification of admissible solutions by solving MLDEs becomes increasingly difficult at higher $\ell$ -- where movable poles and accessory parameters appear. In this work we introduce differential operators that relate higher-$\ell$ solutions to lower-$\ell$ ones while preserving modular covariance and integrality of the \(q\)-series. In rank two, this generates all allowed Wronskian sectors from the Mathur--Mukhi--Sen equation. In rank three and higher, it reduces the construction of higher-$\ell$ quasi-characters to simpler equations with lower $\ell$. This gives an efficient new route for organising candidate RCFT characters, and more generally quasi-characters, across the Wronskian tower. As an application, we apply our construction to prove a previously conjectured property on the signs of $\ell=2$ quasi-characters in rank 2.
Comments47 pages (including references). v2: minor changes to appendices and main text, typos corrected, main results unchanged
