论文标题
封闭几何晶体的微分方程
Differential equations for the closed geometric crystal chains
论文作者
论文摘要
我们提出了两种类型的微分方程系统，它们可以从一组离散的集成系统中得出，我们称之为封闭的几何晶体链。一种是一种扩展的Lotka-Volterra系统，另一个似乎是新的，但在特殊情况下会减少到以前已知的系统。这两个方程式都具有与所谓的循环基本对称函数相关的松弛表示，最初引入了它们，以描述仿射A型几何晶体的产物用于对称张量表示。详细描述了从离散时间的连续时间松弛方程的衍生示例，其中使用了PUISEUX系列扩展中Lax矩阵特征值的渐近行为来实现连续限制的新方法。
We present two types of systems of differential equations that can be derived from a set of discrete integrable systems which we call the closed geometric crystal chains. One is a kind of extended Lotka-Volterra systems, and the other seems to be generally new but reduces to a previously known system in a special case. Both equations have Lax representations associated with what are known as the loop elementary symmetric functions, which were originally introduced to describe products of affine type A geometric crystals for symmetric tensor representations. Examples of the derivations of the continuous time Lax equations from a discrete time one are described in detail, where a novel method of taking a continuum limit by assuming asymptotic behaviors of the eigenvalues of the Lax matrix in Puiseux series expansions is used.
