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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 197, Number 3, Pages 417–434
DOI: https://doi.org/10.4213/tmf9625 (Mi tmf9625) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Calogero–Moser model and $R$-matrix identities

A. V. Zotov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (610 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf9625
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).
Received: 04.09.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 197, Issue 3, Pages 1755–1770
DOI: https://doi.org/10.1134/S0040577918120061
Bibliographic databases:
Document Type: Article
Language: Russian
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
  • https://www.mathnet.ru/eng/tmf/v197/i3/p417
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:42
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