论文标题
从几何$ r $ -matrix转换中的群集集成系统中的离散动力学
Discrete dynamics in cluster integrable systems from geometric $R$-matrix transformations
论文作者
论文摘要
群集可集成的系统是一类广泛的集成系统，该系统在圆环上的两部分二聚体模型上建模。许多离散的集成动力学通过应用局部变换的序列而产生，从而形成了群集集成系统的群集模块化组。该集群模块化组最近以第一作者和Inchiostro为特征。存在一些离散的集成动力学，可以利用与几何$ r $ - matrices相关的非本地转换。在本文中，我们表征了广义群集模块化组（包括局部和非本地转换）在扩展的仿射对称组方面。我们还描述了广义群集模块组对与集群集成系统相关的光谱数据的作用。
Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group of the cluster integrable system. This cluster modular group was recently characterized by the first author and Inchiostro. There exist some discrete integrable dynamics that make use of non-local transformations associated with geometric $R$-matrices. In this article we characterize the generalized cluster modular group -- which includes both local and non-local transformations -- in terms of extended affine symmetric groups. We also describe the action of the generalized cluster modular group on the spectral data associated with cluster integrable systems.
