发表机构
National Research University Higher School of Economics; Skolkovo Institute of Science and Technology（国立高等经济大学; 斯科尔科沃科学技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于上同调场论构造量子层级，提出量子ILW层级极限与Nazarov--Sklyanin层级关系的猜想，并通过多种验证支持。
AI 中文摘要
在P. Rossi和第一作者早前的一篇论文中，提出了构造一大类量子层级的方案，其输入数据由任意上同调场论给出。该构造中，稳定曲线模空间上的双分歧（DR）环扮演了关键角色。作为特例，可得到中间长波（ILW）方程层级的量子化。ILW方程有两个著名的极限：Korteweg--de Vries方程和Benjamin--Ono（BO）方程，对于后者，Nazarov和Sklyanin构造了一个量子层级。在我们的论文中，我们提出了一个猜想，描述量子ILW层级的一个极限与Nazarov--Sklyanin层级之间的关系，并给出了支持该猜想的多种验证。
英文摘要
In an earlier paper of P. Rossi and the first author, a construction of a wide class of quantum hierarchies was presented, with the input data given by an arbitrary cohomological field theory. A crucial role in the construction is played by the double ramification (DR) cycles on the moduli spaces of stable curves. As a special case, one gets a quantization of the hierarchy of the Intermediate Long Wave (ILW) equation. The ILW equation has two famous limits: the Korteweg--de Vries equation and the Benjamin--Ono (BO) equation, and for the latter one a quantum hierarchy was constructed by Nazarov and Sklyanin. In our paper, we propose a conjecture describing a relation between a limit of the quantum ILW hierarchy and the Nazarov--Sklyanin hierarchy and present various checks to support it.
Comments22 pages
