Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
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


Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 2, Pages 176–185
DOI: https://doi.org/10.4213/tmf9097
(Mi tmf9097)
 

This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (500 kB) Citations (7)
References:
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.
Received: 08.11.2015
Revised: 18.12.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 2, Pages 1554–1562
DOI: https://doi.org/10.1134/S0040577916110027
Bibliographic databases:
Document Type: Article
Language: Russian
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://mathscinet.ams.org/mathscinet-getitem?mr=3589028}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...189.1554Z}
\elib{https://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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000389995500002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85002750241}
Linking options:
  • https://www.mathnet.ru/eng/tmf9097
  • https://doi.org/10.4213/tmf9097
  • https://www.mathnet.ru/eng/tmf/v189/i2/p176
  • Related presentations:
    This publication is cited in the following 7 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
    Statistics & downloads:
    Abstract page:364
    Full-text PDF :119
    References:51
    First page:11
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024