论文标题
量子KDV层次结构和准模型形式
Quantum KdV hierarchy and quasimodular forms
论文作者
论文摘要
杜布罗文（Dubrovin）表明，无分散korteweg-de vries（KDV）层次结构的量化频谱（相对于第一个泊松结构）的光谱是由移动的对称函数给出的；后者由Bloch-Okounkov定理与整个模块化组上的半模拟形式相关。我们将与准形式的关系扩展到完整的量子KDV层次结构（以及更通用的量子中间长波层次结构）。这些量子整合的层次结构已由曲线模量空间中的双重分支周期定义了Buryak和Rossi的定义。本文的主要工具和概念贡献是对准则的一般有效标准。
Dubrovin has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg-de Vries (KdV) hierarchy is given by shifted symmetric functions; the latter are related by the Bloch-Okounkov Theorem to quasimodular forms on the full modular group. We extend the relation to quasimodular forms to the full quantum KdV hierarchy (and to the more general quantum Intermediate Long Wave hierarchy). These quantum integrable hierarchies have been defined by Buryak and Rossi in terms of the Double Ramification cycle in the moduli space of curves. The main tool and conceptual contribution of the paper is a general effective criterion for quasimodularity.
