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

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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 1, Pages 55–67
DOI: https://doi.org/10.4213/tmf9925 (Mi tmf9925)

This article is cited in 6 scientific papers (total in 6 papers)

Integrable system of generalized relativistic interacting tops

I. A. Sechin^ab, A. V. Zotov^a

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

Full-text PDF (476 kB) Citations (6)

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

Abstract: We describe a family of integrable

G L (N M)

$GL(NM)$ models generalizing classical spin Ruijsenaars–Schneider systems (the case

N = 1

$N=1$ ) on one hand and relativistic integrable tops on the

G L (N)

$GL(N)$ Lie group (the case

M = 1

$M=1$ ) 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

G L (N)

$GL(N)$

R

$R$ -matrix in the fundamental representation of

G L (N)

$GL(N)$ .

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).

Received: 27.04.2020
Revised: 27.04.2020

English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 1, Pages 1291–1302
DOI: https://doi.org/10.1134/S0040577920100049

Bibliographic databases:

Document Type: Article

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/tmf9925

https://doi.org/10.4213/tmf9925

https://www.mathnet.ru/eng/tmf/v205/i1/p55

This publication is cited in the following 6 articles:

Maxime Fairon, “Integrable systems on multiplicative quiver varieties from cyclic quivers”, J. Phys. A: Math. Theor., 58:4 (2025), 045202
M. Matushko, A. Zotov, “Supersymmetric generalization of $q$ -deformed long-range spin chains of Haldane–Shastry type and trigonometric $\mathrm{GL}(N|M)$ solution of associative Yang–Baxter equation”, Nuclear Phys. B, 1001 (2024), 116499–14
K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$ -matrix: IRF–vertex relations and the associative Yang–Baxter equation”, Theoret. and Math. Phys., 216:2 (2023), 1083–1103
M. G. Matushko, A. V. Zotov, “On the $R$ -matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators”, Theoret. and Math. Phys., 213:2 (2022), 1543–1559
A. V. Zotov, E. S. Trunina, “Lax equations for relativistic $\mathrm{G}\mathrm{L}(NM,\mathbb{C})$ Gaudin models on elliptic curve”, J. Phys. A, 55:39 (2022), 395202–31
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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