E. S. Trunina, A. V. Zotov, “Multi-pole extension of the elliptic models of interacting integrable tops”, TMF, 209:1 (2021), 16–45; Theoret. and Math. Phys., 209:1 (2021), 1331

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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 209, Number 1, Pages 16–45
DOI: https://doi.org/10.4213/tmf10114 (Mi tmf10114)

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

Multi-pole extension of the elliptic models of interacting integrable tops

E. S. Trunina^ab, A. V. Zotov^a

^a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
^b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow region, Russia

Full-text PDF (739 kB) Citations (6)

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DOI: https://doi.org/10.4213/tmf10114

Abstract: We review and give a detailed description of the

g l_{N M}

$gl_{NM}$ Gaudin models related to holomorphic vector bundles of rank

N M

$NM$ and degree

N

$N$ over an elliptic curve with

n

$n$ punctures. We introduce their generalizations constructed by means of

R

$R$ -matrices satisfying the associative Yang–Baxter equation. A natural extension of the obtained models to the Schlesinger systems is also given.

Keywords: elliptic integrable system, elliptic Schlesinger system, Gaudin model.

Funding agency	Grant number
Russian Science Foundation	19-11-00062
This work is supported by the Russian Science Foundation under grant 19-11-00062 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.

Received: 19.04.2021
Revised: 20.05.2021

English version:
Theoretical and Mathematical Physics, 2021, Volume 209, Issue 1, Pages 1331–1356
DOI: https://doi.org/10.1134/S0040577921100020

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: E. S. Trunina, A. V. Zotov, “Multi-pole extension of the elliptic models of interacting integrable tops”, TMF, 209:1 (2021), 16–45; Theoret. and Math. Phys., 209:1 (2021), 1331–1356

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf10114

https://doi.org/10.4213/tmf10114

https://www.mathnet.ru/eng/tmf/v209/i1/p16

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
M. A. Olshanetsky, A. V. Zotov, A. M. Levin, “2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles”, Eur. Phys. J. C, Part. Fields, 82 (2022), 635–14

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

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