论文标题
在周期性边界条件下，可集成的蜂窝自动机的几何提升
Geometric lifting of the integrable cellular automata with periodic boundary conditions
论文作者
论文摘要
受G. Frieden最近在与矩形年轻Tableaux相关的A型A型晶体的几何R-Matrix上的工作启发，我们提出了一种构建一种新型离散集成系统系列的方法，可以将其视为广义周期性盒球系统的几何提升。通过转换矩阵的常规用法来定义离散周期性TODA链的LAX表示，并巧妙地使用了Perron-Frobonious Theorem，我们给出了系统的定义。它是在真正的正相关变量的空间上进行的，而没有通过自变量的无缩写合理函数编写它们，但仍具有可以热带化的保守量。我们证明，在此设置中，一个盒子式系统系统的“载体”类似物的方程式，以确保其周期性边界条件始终具有独特的解决方案。结果，我们系统中的任何州都承认，与任何矩形形状的tableaux相关的通勤家庭演变与相应的通用周期性盒球系统相比，某些州没有承认某些时间的演变。
Inspired by G. Frieden's recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel family of discrete integrable systems which can be regarded as a geometric lifting of the generalized periodic box-ball systems. By converting the conventional usage of the matrices for defining the Lax representation of the discrete periodic Toda chain, together with a clever use of the Perron-Frobenious theorem, we give a definition of our systems. It is carried out on the space of real positive dependent variables, without regarding them to be written by subtraction-free rational functions of independent variables but nevertheless with the conserved quantities which can be tropicalized. We prove that, in this setup an equation of an analogue of the `carrier' of the box-ball system for assuring its periodic boundary condition always has a unique solution. As a result, any states in our systems admit a commuting family of time evolutions associated with any rectangular shaped tableaux, in contrast to the case of corresponding generalized periodic box-ball systems where some states did not admit some of such time evolutions.
