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TMF, 1984, Volume 61, Number 2, Pages 163–173 (Mi tmf5681)  

This article is cited in 9 scientific papers (total in 9 papers)

Structure of quantum L operators for the R matrix of the XXZ model

V. O. Tarasov


Abstract: For the R matrices of the XXX and XXZ models, a study is made of the L operators, i.e., the monodromy matrices with vacuum and finite-dimensional single-particle subspace. All possible vacuum eigenvalues of the diagonal matrix elements are found for such monodromy matrices. In the case of the R matrix of the XXZ model, the ratio of the vacuum eigenvalues is shown to be $\pi$-periodic with respect to the spectral parameter. All monodromy matrices with one-dimensional single-particle subspace are found.

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English version:
Theoretical and Mathematical Physics, 1984, 61:2, 1065–1072

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Received: 01.11.1983

Citation: V. O. Tarasov, “Structure of quantum L operators for the R matrix of the XXZ model”, TMF, 61:2 (1984), 163–173; Theoret. and Math. Phys., 61:2 (1984), 1065–1072

Citation in format AMSBIB
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\by V.~O.~Tarasov
\paper Structure of quantum L operators for the R matrix of the XXZ model
\jour TMF
\yr 1984
\vol 61
\issue 2
\pages 163--173
\mathnet{http://mi.mathnet.ru/tmf5681}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=778541}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 2
\pages 1065--1072
\crossref{https://doi.org/10.1007/BF01029107}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AKD1300001}


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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. V. O. Tarasov, “Irreducible monodromy matrices for the $R$ matrix of the $XXZ$ model and local lattice quantum Hamiltonians”, Theoret. and Math. Phys., 63:2 (1985), 440–454  mathnet  crossref  mathscinet  isi
    2. A. I. Molev, M. L. Nazarov, G. I. Olshanskii, “Yangians and classical Lie algebras”, Russian Math. Surveys, 51:2 (1996), 205–282  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. V. A. Stukopin, “O predstavleniyakh yangiana superalgebry Li $\mathfrak{sl}(1,2)$”, Vladikavk. matem. zhurn., 13:3 (2011), 53–63  mathnet
    4. Bazhanov V.V., Frassek R., Lukowski T., Meneghelli C., Staudacher M., “Baxter Q-operators and representations of Yangians”, Nuclear Phys B, 850:1 (2011), 148–174  crossref  isi
    5. Stukopin V.A., “O klassifikatsii neprivodimykh predstavlenii yangiana superalgebry li \it{sl} (1, 2)”, Vestnik donskogo gosudarstvennogo tekhnicheskogo universiteta, 11 (2011), 1180–1184  elib
    6. Chicherin D., Derkachov S., Karakhanyan D., Kirschner R., “Baxter operators for arbitrary spin II”, Nuclear Phys B, 854:2 (2012), 433–465  crossref  isi
    7. Khoroshkin S. Nazarov M., “Mickelsson Algebras and Representations of Yangians”, Trans. Am. Math. Soc., 364:3 (2012), 1293–1367  isi
    8. V. A. Stukopin, “Representations of the Yangian of a Lie superalgebra of type $A(m,n)$”, Izv. Math., 77:5 (2013), 1021–1043  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. Stukopin V., Xxv International Conference on Integrable Systems and Quantum Symmetries (Isqs-25), Journal of Physics Conference Series, 965, IOP Publishing Ltd, 2018  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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