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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 213, Number 2, Pages 268–286
DOI: https://doi.org/10.4213/tmf10351 (Mi tmf10351) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the $R$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators

M. G. Matushkoab, A. V. Zotovac

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Center for Advanced Studies, Skolkovo Institute of Science and Technology, Moscow, Russia
c Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf10351
Abstract: We propose and prove a set of identities for the elliptic $GL_M$ $R$-matrix (in the fundamental representation). In the scalar case ($M=1$), these are elliptic function identities derived by Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying the construction of integral solutions of quantum spinless Ruijsenaars–Schneider model. In this respect, our result can be regarded as a first step toward constructing solutions of the quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.
Keywords: quantum integrable spin many-body system, spin Ruijsenaars–Schneider model, $R$-matrix identities, kernel identity.
Funding agency Grant number
Russian Science Foundation 20-41-09009
The work of M. G. Matushko was partially supported by the Russian Science Foundation (project 20-41-09009).
Received: 16.08.2022
Revised: 16.08.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 213, Issue 2, Pages 1543–1559
DOI: https://doi.org/10.1134/S0040577922110046
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. G. Matushko, A. V. Zotov, “On the $R$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators”, TMF, 213:2 (2022), 268–286; Theoret. and Math. Phys., 213:2 (2022), 1543–1559
Citation in format AMSBIB
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\by M.~G.~Matushko, A.~V.~Zotov
\paper On the~$R$-matrix identities related to elliptic anisotropic
spin Ruijsenaars--Macdonald operators
\jour TMF
\yr 2022
\vol 213
\issue 2
\pages 268--286
\mathnet{http://mi.mathnet.ru/tmf10351}
\crossref{https://doi.org/10.4213/tmf10351}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538869}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022TMP...213.1543M}
\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 213
\issue 2
\pages 1543--1559
\crossref{https://doi.org/10.1134/S0040577922110046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85142428679}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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