论文标题
广义ILW层次结构：扩展晶格GD层次结构的解决方案和限制
Generalized ILW hierarchy: Solutions and limit to extended lattice GD hierarchy
论文作者
论文摘要
中间长波（ILW）层次结构及其概括，标记为正整数$ n $，可以作为晶格KP层次结构的降低。晶格KP层次结构的集成性由这些还原的系统继承。特别是，所有解决方案都可以通过差异操作员的分解问题来捕获。它们中有一个特殊的解决方案是从Okounkov和Pandharipande的pressing oters获得的，用于$ \ Mathbb {cp}^1 $的Equivariant Gromov-Witten理论。这表明具有模棱两可的TODA层次结构的隐藏链接。广义的ILW层次结构也与晶格Gelfand-Dickey（GD）层次结构及其通过对数流相关。对数流可以从广义ILW层次结构得出缩放限制，作为系统的参数倾向于$ 0 $。这解释了对数流的起源。 toda层次结构的类似缩放限制得出了扩展的1D/Bigraded Toda层次结构。
The intermediate long wave (ILW) hierarchy and its generalization, labelled by a positive integer $N$, can be formulated as reductions of the lattice KP hierarchy. The integrability of the lattice KP hierarchy is inherited by these reduced systems. In particular, all solutions can be captured by a factorization problem of difference operators. A special solution among them is obtained from Okounkov and Pandharipande's dressing operators for the equivariant Gromov-Witten theory of $\mathbb{CP}^1$. This indicates a hidden link with the equivariant Toda hierarchy. The generalized ILW hierarchy is also related to the lattice Gelfand-Dickey (GD) hierarchy and its extension by logarithmic flows. The logarithmic flows can be derived from the generalized ILW hierarchy by a scaling limit as a parameter of the system tends to $0$. This explains an origin of the logarithmic flows. A similar scaling limit of the equivariant Toda hierarchy yields the extended 1D/bigraded Toda hierarchy.
