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Integrable system of generalized relativistic interacting tops
Theoretical and Mathematical Physics ( IF 1 ) Pub Date : 2020-10-01 , DOI: 10.1134/s0040577920100049
I. A. Sechin , A. V. Zotov

A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie group (the case $M=1$). The described models are obtained by means of the Lax pair with spectral parameter. Equations of motion are derived. For the construction of the Lax representation the $GL(N)$ $R$--matrix in the fundamental representation of $GL(N)$ is used.

中文翻译:

广义相对论相互作用顶的可积系统

描述了一系列可积分的 $GL(NM)$ 模型。一方面它推广了经典自旋 Ruijsenaars--Schneider 系统(情况 $N=1$),另一方面它推广了 $GL(N)$ 李群上的相对论可积顶(情况 $M= 1 美元)。所描述的模型是通过具有光谱参数的 Lax 对获得的。推导出运动方程。对于 Lax 表示的构造,使用了 $GL(N)$ 的基本表示中的 $GL(N)$ $R$--matrix。
更新日期:2020-10-01
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