论文标题
相对论$ {\ rm gl}（nm，{\ mathbb c}）$ gaudin模型上椭圆曲线上的LAX方程
Lax equations for relativistic ${\rm GL}(NM,{\mathbb C})$ Gaudin models on elliptic curve
论文作者
论文摘要
我们描述了最通用的$ {\ rm gl} _ {nm} $经典的椭圆有限二维整合系统，lax矩阵在椭圆曲线上具有$ n $简单的极点。对于$ m = 1 $，它重现了经典的不均匀自旋链，以$ n = 1 $，它是旋转ruijsenaars-Schneider模型的Gaudin型（Multispin）扩展，对于$ n = 1 $，$ n = 1 $ $ m $互动相互作用的相对性$ {\ rm lm gl} _n $ gl} _n $ gl} _n $ tops eark in Doseps ears in Somewseps ears in Somewseps ears in Somewseps ears in Somewepers ears in lose eperes in lose epres in lose eperes in Somewsepe ears in Somewsepes中。通过这种方式，我们在$ {\ rm gl} $ - 椭圆曲线上捆绑了相对论高丁模型的分类。作为副产品，我们描述了不均匀的Ruijsenaars链。我们表明，当Lax矩阵的残基是等级的一号时，该模型可以被视为多刺ruijsenaars-Schneider模型的特定情况。对于此模型，获得了通过规范变量的经典自旋变量的明确参数化。最后，最通用的$ {\ rm gl} _ {nm} $模型也通过$ r $ - matrices来描述，使Yang-baxter方程满足。此描述提供了$ {\ rm gl} _ {nm} $模型的三角类似物。
We describe the most general ${\rm GL}_{NM}$ classical elliptic finite-dimensional integrable system, which Lax matrix has $n$ simple poles on elliptic curve. For $M=1$ it reproduces the classical inhomogeneous spin chain, for $N=1$ it is the Gaudin type (multispin) extension of the spin Ruijsenaars-Schneider model, and for $n=1$ the model of $M$ interacting relativistic ${\rm GL}_N$ tops emerges in some particular case. In this way we present a classification for relativistic Gaudin models on ${\rm GL}$-bundles over elliptic curve. As a by-product we describe the inhomogeneous Ruijsenaars chain. We show that this model can be considered as a particular case of multispin Ruijsenaars-Schneider model when residues of the Lax matrix are of rank one. An explicit parametrization of the classical spin variables through the canonical variables is obtained for this model. Finally, the most general ${\rm GL}_{NM}$ model is also described through $R$-matrices satisfying associative Yang-Baxter equation. This description provides the trigonometric and rational analogues of ${\rm GL}_{NM}$ models.
