论文标题
仿射Weyl组的翻译及其在离散集成系统中的应用
Translations in affine Weyl groups and their applications in discrete integrable systems
论文作者
论文摘要
在本文中，我们回顾了与离散集成系统研究相关的Weyl组的属性和表示。以前在\ cite {jns4，shi：19}中，显示出$ ade $的Weyl off ode $（被称为简单）的属性可用于表征和建立不同集成系统之间的关系。在这里，我们将配方和讨论扩展到包括非简化类型的类型，特别注意开发与仿生基团的翻译元素相关的公式。作为应用程序，我们展示了如何用于阐明某些类型的$ e_8 $ \ cite {nn_elliptic}和$ f_4 $ \ cite {ahjn：16}的类型的集成系统的本质。
In this paper, we review the properties and representations of the Weyl groups relevant in the study of discrete integrable systems. Previously in \cite{jns4, Shi:19}, properties of Weyl groups of type $ADE$ (known as simply-laced) were shown to be useful in characterizing and establishing relations between different integrable systems. Here we extend the formulations and discussions to include non-simply-laced types, giving special attention to developing formulas related to the translational elements of the affine Weyl groups. As applications, we show how these are used to clarify the natures of some integrable systems of type $E_8$ \cite{NN_elliptic} and $F_4$ \cite{ahjn:16} appeared recently in the literature.
