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TMF, 2018, Volume 197, Number 3, Pages 417–434 (Mi tmf9625)  

This article is cited in 4 scientific papers (total in 4 papers)

Calogero–Moser model and $R$-matrix identities

A. V. Zotov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We discuss properties of $R$-matrix-valued Lax pairs for the elliptic Calogero-Moser model. In particular, we show that the family of Hamiltonians arising from this Lax representation contains only known Hamiltonians and no others. We review the relation of $R$-matrix-valued Lax pairs to Hitchin systems on bundles with nontrivial characteristic classes over elliptic curves and also to quantum long-range spin chains. We prove a general higher-order identity for solutions of the associative Yang–Baxter equation.

Keywords: elliptic integrable system, long-range spin chain, associative Yang–Baxter equation.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This research is supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).


DOI: https://doi.org/10.4213/tmf9625

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English version:
Theoretical and Mathematical Physics, 2018, 197:3, 1755–1770

Bibliographic databases:

Received: 04.09.2018

Citation: A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, TMF, 197:3 (2018), 417–434; Theoret. and Math. Phys., 197:3 (2018), 1755–1770

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9625
  • http://mi.mathnet.ru/eng/tmf/v197/i3/p417

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

    This publication is cited in the following articles:
    1. A. Grekov, I. Sechin, A. Zotov, “Generalized model of interacting integrable tops”, J. High Energy Phys., 2019, no. 10, 081  crossref  mathscinet  isi
    2. I. A. Sechin, A. V. Zotov, “Integrable system of generalized relativistic interacting tops”, Theoret. and Math. Phys., 205:1 (2020), 1291–1302  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetric Kronecker elliptic function and Yang-Baxter equations”, J. Math. Phys., 61:10 (2020), 103504  crossref  mathscinet  zmath  isi
    4. A. Levin, M. Olshanetsky, A. Zotov, “Odd supersymmetrization of elliptic r-matrices”, J. Phys. A-Math. Theor., 53:18 (2020), 185202  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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