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TMF, 2013, Volume 174, Number 1, Pages 25–45 (Mi tmf8352)  

This article is cited in 12 scientific papers (total in 12 papers)

Universal integrability objects

H. Boosa, F. Gohmanna, A. Klümpera, Kh. Nirovba, A. V. Razumovcd

a University of Wuppertal
b Institute for Nuclear Research, RAS, Moscow, Russia
c Max-Planck-Institut für Mathematik, Bonn, Germany
d Institute for High Energy Physics, Protvino, Moscow Oblast, Russia

Abstract: We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal L(\mathfrak{sl}_2))$. We give a complete set of the functional relations correcting inexactitudes in the previous considerations. We especially attend to the interrelation of the representations used to construct the universal transfer operators and $Q$-operators.

Keywords: integrable system, quantum group, representation, functional relation

DOI: https://doi.org/10.4213/tmf8352

Full text: PDF file (589 kB)
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English version:
Theoretical and Mathematical Physics, 2013, 174:1, 21–39

Bibliographic databases:


Citation: H. Boos, F. Gohmann, A. Klümper, Kh. Nirov, A. V. Razumov, “Universal integrability objects”, TMF, 174:1 (2013), 25–45; Theoret. and Math. Phys., 174:1 (2013), 21–39

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Razumov, “Monodromy operators for higher rank”, J. Phys. A-Math. Theor., 46:38 (2013), 385201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. K. Motegi, “On Baxter's $Q$ operator of the higher spin XXZ chain at the Razumov-Stroganov point”, J. Math. Phys., 54:6 (2013), 063510  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. D. Buecher, I. Runkel, “Integrable perturbations of conformal field theories and Yetter-Drinfeld modules”, J. Math. Phys., 55:11 (2014), 111705  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. V. V. Mangazeev, “$Q$-operators in the six-vertex model”, Nucl. Phys. B, 886 (2014), 166–184  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. H. Boos, F. Goehmann, A. Kluemper, Kh. S. Nirov, A. V. Razumov, “Quantum groups and functional relations for higher rank”, J. Phys. A-Math. Theor., 47:27 (2014), 275201  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. V. V. Mangazeev, “On the Yang–Baxter equation for the six-vertex model”, Nucl. Phys. B, 882 (2014), 70–96  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. A. A. Ovchinnikov, “Baxter $Q$-operator and functional relations”, Phys. Lett. B, 742 (2015), 335–339  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. H. Boos, F. Goehmann, A. Kluemper, Kh. S. Nirov, A. V. Razumov, “Oscillator versus prefundamental representations”, J. Math. Phys., 57:11 (2016), 111702  crossref  mathscinet  zmath  isi  elib  scopus
    9. Kh. S. Nirov, A. V. Razumov, J. Geom. Phys., 112 (2017), 1–28  crossref  mathscinet  zmath  isi  elib  scopus
    10. Khazret S. Nirov, Alexander V. Razumov, “Highest $\ell$-Weight Representations and Functional Relations”, SIGMA, 13 (2017), 043, 31 pp.  mathnet  crossref
    11. H. Boos, F. Goehmann, A. Kluemper, Kh. S. Nirov, A. V. Razumov, “Oscillator versus prefundamental representations. II: arbitrary higher ranks”, J. Math. Phys., 58:9 (2017), 093504  crossref  mathscinet  zmath  isi  scopus
    12. Kh. S. Nirov, A. V. Razumov, “Quantum groups, verma modules and $q$-oscillators: general linear case”, J. Phys. A-Math. Theor., 50:30 (2017), 305201  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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