This article is cited in 7 papers

Integrable system of generalized relativistic interacting tops

I. A. Sechin^ab, A. V. Zotov<sup>a

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
^b Center for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia

Abstract: We describe a family of integrable $GL(NM)$ models generalizing classical spin Ruijsenaars–Schneider systems (the case $N=1$) on one hand and relativistic integrable tops on the $GL(N)$ Lie group (the case $M=1$) on the other hand. We obtain the described models using the Lax pair with a spectral parameter and derive the equations of motion. To construct the Lax representation, we use the $GL(N)$ $R$-matrix in the fundamental representation of $GL(N)$.

Keywords: elliptic integrable system, spin Ruijsenaars–Schneider model, integrable interacting tops.

Received: 27.04.2020
Revised: 27.04.2020

DOI: 10.4213/tmf9925

 English version: Theoretical and Mathematical Physics, 2020, 205:1, 1291–1302

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