RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2016, Volume 189, Number 2, Pages 176–185 (Mi tmf9097)  

This article is cited in 5 scientific papers (total in 5 papers)

Higher-order analogues of the unitarity condition for quantum $R$-matrices

A. V. Zotov

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

Abstract: We derive a family of $n$th-order identities for quantum $R$-matrices of the Baxter–Belavin type in the fundamental representation. The set of identities includes the unitarity condition as the simplest case $(n=2)$. Our study is inspired by the fact that the third-order identity provides commutativity of the Knizhnik–Zamolodchikov–Bernard connections. On the other hand, the same identity yields the $R$-matrix-valued Lax pairs for classical integrable systems of Calogero type, whose construction uses the interpretation of the quantum $R$-matrix as a matrix generalization of the Kronecker function. We present a proof of the higher-order scalar identities for the Kronecker functions, which is then naturally generalized to $R$-matrix identities.

Keywords: classical integrable system, $R$-matrix Lax representation, duality

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/tmf9097

Full text: PDF file (500 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2016, 189:2, 1554–1562

Bibliographic databases:

ArXiv: 1511.02468
Received: 08.11.2015
Revised: 18.12.2015

Citation: A. V. Zotov, “Higher-order analogues of the unitarity condition for quantum $R$-matrices”, TMF, 189:2 (2016), 176–185; Theoret. and Math. Phys., 189:2 (2016), 1554–1562

Citation in format AMSBIB
\Bibitem{Zot16}
\by A.~V.~Zotov
\paper Higher-order analogues of the~unitarity condition for quantum $R$-matrices
\jour TMF
\yr 2016
\vol 189
\issue 2
\pages 176--185
\mathnet{http://mi.mathnet.ru/tmf9097}
\crossref{https://doi.org/10.4213/tmf9097}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3589028}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...189.1554Z}
\elib{http://elibrary.ru/item.asp?id=27485049}
\transl
\jour Theoret. and Math. Phys.
\yr 2016
\vol 189
\issue 2
\pages 1554--1562
\crossref{https://doi.org/10.1134/S0040577916110027}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000389995500002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85002750241}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9097
  • https://doi.org/10.4213/tmf9097
  • http://mi.mathnet.ru/eng/tmf/v189/i2/p176

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    Related presentations:

    This publication is cited in the following articles:
    1. I. Sechin, A. Zotov, “Associative Yang–Baxter equation for quantum (semi-)dynamical R-matrices”, J. Math. Phys., 57:5 (2016), 053505, 14 pp.  crossref  mathscinet  zmath  isi  scopus
    2. A. Zotov, “Relativistic elliptic matrix tops and finite Fourier transformations”, Mod. Phys. Lett. A, 32:32 (2017), 1750169, 22 pp.  crossref  mathscinet  zmath  isi  scopus
    3. A. Grekov, A. Zotov, “On $R$-matrix valued Lax pairs for Calogero–Moser models”, J. Phys. A-Math. Theor., 51:31 (2018), 315202  crossref  isi  scopus
    4. I. Sechin, A. Zotov, “$R$-matrix valued Lax pairs and long-range spin chains”, Phys. Lett. B, 781 (2018), 1–7  crossref  mathscinet  isi  scopus
    5. A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:199
    References:22
    First page:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019