论文标题
$（n+1）（2N+1）$ - 顶点模型的杨巴克斯特方程的解决方案通过差分方法
The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach
论文作者
论文摘要
在这些参数的某个固定点上评估的杨 - 巴克斯特方程相对于其光谱参数的形式衍生物为我们提供了两个微分方程系统。但是，$ r $矩阵元素的衍生物可以被视为独立变量，并从系统中删除，然后获得了两个多项式方程式系统。通常，这些多项式系统具有非零的希尔伯特维度，这意味着并非R矩阵的所有元素都可以通过它们固定。然而，可以通过求解作为该方法一致性条件的几个简单微分方程来找到其余未知数。该方法也可以轻松地分析解决方案的分支，从而确保解决方案的独特性和通用性。在这项工作中，我们考虑了$（n+1）（2n+1）$ - 顶点模型的Yang-Baxter方程，其基于$ a_n $对称的概括。这种差异方法使我们能够以系统的方式求解Yang-Baxter方程。
The formal derivatives of the Yang-Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the $R$ matrix elements, however, can be regarded as independent variables and eliminated from the systems, after which two systems of polynomial equations are obtained in place. In general, these polynomial systems have a non-zero Hilbert dimension, which means that not all elements of the R matrix can be fixed through them. Nevertheless, the remaining unknowns can be found by solving a few number of simple differential equations that arise as consistency conditions of the method. The branches of the solutions can also be easily analyzed by this method, which ensures the uniqueness and generality of the solutions. In this work we considered the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models with a generalization based on the $A_n$ symmetry. This differential approach allowed us to solve the Yang-Baxter equation in a systematic way.
