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TMF, 2020, Volume 205, Number 1, Pages 55–67 (Mi tmf9925)  

This article is cited in 1 scientific paper (total in 1 paper)

Integrable system of generalized relativistic interacting tops

I. A. Sechinab, A. V. Zotova*

a 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.

Funding Agency Grant Number
Russian Science Foundation 19-11-00062
This research (including the results in Sec. 2) was performed at the Steklov Mathematical Institute of Russian Academy of Sciences and is supported by a grant from the Russian Science Foundation (Project No. 19-11-00062).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9925

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

Bibliographic databases:

Received: 27.04.2020
Revised: 27.04.2020

Citation: I. A. Sechin, A. V. Zotov, “Integrable system of generalized relativistic interacting tops”, TMF, 205:1 (2020), 55–67; Theoret. and Math. Phys., 205:1 (2020), 1291–1302

Citation in format AMSBIB
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\paper Integrable system of generalized relativistic interacting tops
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\pages 55--67
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\jour Theoret. and Math. Phys.
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\vol 205
\issue 1
\pages 1291--1302
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  • https://doi.org/10.4213/tmf9925
  • http://mi.mathnet.ru/eng/tmf/v205/i1/p55

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Sechin, A. V. Zotov, “Quadratic algebras based on $SL(NM)$ elliptic quantum $R$-matrices”, Theoret. and Math. Phys., 208:2 (2021), 1156–1164  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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