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

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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 1, Pages 25–45
DOI: https://doi.org/10.4213/tmf8352 (Mi tmf8352)

This article is cited in 23 scientific papers (total in 23 papers)

Universal integrability objects

H. Boos^a, F. Gohmann^a, A. Klümper^a, Kh. Nirov^ba, A. V. Razumov^cd

^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

Full-text PDF (589 kB) Citations (23)

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

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.

English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 1, Pages 21–39
DOI: https://doi.org/10.1007/s11232-013-0002-8

Bibliographic databases:

Document Type: Article

Language: Russian

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

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This publication is cited in the following 23 articles:

Alec Cooper, Bart Vlaar, Robert Weston, “A Q-Operator for Open Spin Chains II: Boundary Factorization”, Commun. Math. Phys., 405:5 (2024)
A. V. Razumov, “Khoroshkin–Tolstoy approach to quantum superalgebras”, Theoret. and Math. Phys., 215:1 (2023), 560–585
A. V. Razumov, “On Poincaré–Birkhoff–Witt basis of the quantum general linear superalgebra”, Theoret. and Math. Phys., 217:3 (2023), 1938–1953
A. V. Razumov, “$\ell$-weights and factorization of transfer operators”, Theoret. and Math. Phys., 208:2 (2021), 1116–1143
Razumov V A., “Quantum Groups and Functional Relations For Arbitrary Rank”, Nucl. Phys. B, 971 (2021), 115517
Razumov V A., “Reduced Qkz Equation and Genuine Qkz Equation”, J. Phys. A-Math. Theor., 53:40 (2020), 405204
Vlaar B., Weston R., “A Q-Operator For Open Spin Chains i. Baxter'S Tq Relation”, J. Phys. A-Math. Theor., 53:24 (2020), 245205
Kluemper A., Nirov Kh.S., Razumov V A., “Reduced Qkz Equation: General Case”, J. Phys. A-Math. Theor., 53:1 (2020), 015202
Khazret S. Nirov, Alexander V. Razumov, “Vertex Models and Spin Chains in Formulas and Pictures”, SIGMA, 15 (2019), 068, 67 pp.
Kh. S. Nirov, A. V. Razumov, J. Geom. Phys., 112 (2017), 1–28
Khazret S. Nirov, Alexander V. Razumov, “Highest $\ell$-Weight Representations and Functional Relations”, SIGMA, 13 (2017), 043, 31 pp.
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
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
Kh.S. Nirov, A.V. Razumov, “Quantum groups and functional relations for lower rank”, Journal of Geometry and Physics, 112 (2017), 1
H. Boos, F. Goehmann, A. Kluemper, Kh. S. Nirov, A. V. Razumov, “Oscillator versus prefundamental representations”, J. Math. Phys., 57:11 (2016), 111702
Kh S Nirov, A V Razumov, “Quantum affine algebras and universal functional relations”, J. Phys.: Conf. Ser., 670 (2016), 012037
A. A. Ovchinnikov, “Baxter $Q$-operator and functional relations”, Phys. Lett. B, 742 (2015), 335–339
D. Buecher, I. Runkel, “Integrable perturbations of conformal field theories and Yetter-Drinfeld modules”, J. Math. Phys., 55:11 (2014), 111705
V. V. Mangazeev, “$Q$-operators in the six-vertex model”, Nucl. Phys. B, 886 (2014), 166–184
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

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

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