J. Avan, P. P. Kulish, G. Rollet, “Reflection $K$-matrices related to Temperley–Lieb $R$-matrices”, TMF, 169:2 (2011), 194–203; Theoret. and Math. Phys., 169:2 (2011), 1530

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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 169, Number 2, Pages 194–203
DOI: https://doi.org/10.4213/tmf6721 (Mi tmf6721)

This article is cited in 12 scientific papers (total in 13 papers)

Reflection

$K$ -matrices related to Temperley–Lieb

$R$ -matrices

J. Avan^a, P. P. Kulish^b, G. Rollet^a

^a Laboratoire de physique théorique et modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, Cergy-Pontoise, France
^b St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

Full-text PDF (429 kB) Citations (13)

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DOI: https://doi.org/10.4213/tmf6721

Abstract: We construct general solutions of the reflection equation associated with Temperley–Lieb

$R$ -matrices. We find their parameterization and obtain the Hamiltonians of the corresponding integrable spin systems.

Keywords: Yang–Baxter equation,

$R$ -matrix, reflection equation, open spin chain.

Received: 19.11.2011

English version:
Theoretical and Mathematical Physics, 2011, Volume 169, Issue 2, Pages 1530–1538
DOI: https://doi.org/10.1007/s11232-011-0130-y

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: J. Avan, P. P. Kulish, G. Rollet, “Reflection

$K$ -matrices related to Temperley–Lieb

$R$ -matrices”, TMF, 169:2 (2011), 194–203; Theoret. and Math. Phys., 169:2 (2011), 1530–1538

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6721

https://doi.org/10.4213/tmf6721

https://www.mathnet.ru/eng/tmf/v169/i2/p194

This publication is cited in the following 13 articles:

Kun Hao, Olof Salberger, Vladimir Korepin, “Exact solution of the quantum integrable model associated with the Motzkin spin chain”, J. High Energ. Phys., 2023:8 (2023)
Tong B., Salberger O., Hao K., Korepin V., “Shor-Movassagh Chain Leads to Unusual Integrable Model”, J. Phys. A-Math. Theor., 54:39 (2021), 394002
Kitanine N. Nepomechie R.I. Reshetikhin N., “Quantum Integrability and Quantum Groups: a Special Issue in Memory of Petr P Kulish”, J. Phys. A-Math. Theor., 51:11 (2018), 110201
Lima-Santos A., “On the $\mathcal{U}_{q}[osp(1|2)]$ Temperley–Lieb Model”, J. Stat. Phys., 165:5 (2016), 953–969
Hutsalyuk A., Liashyk A., Pakuliak S.Z., Ragoucy E., Slavnov N.A., “Scalar products of Bethe vectors in models with ${\mathfrak{gl}}(2| 1)$ symmetry 1. Super-analog of Reshetikhin formula”, J. Phys. A-Math. Theor., 49:45 (2016), 454005, 1–28
Nepomechie R.I., Pimenta R.A., “Algebraic Bethe ansatz for the Temperley–Lieb spin-1 chain”, Nucl. Phys. B, 910 (2016), 885–909
Nepomechie R.I., Pimenta R.A., “Universal Bethe ansatz solution for the Temperley–Lieb spin chain”, Nucl. Phys. B, 910 (2016), 910–928
“Osnovnye nauchnye trudy Petra Petrovicha Kulisha”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 23, Zap. nauchn. sem. POMI, 433, POMI, SPb., 2015, 8–19
J. Avan, T. Fonseca, L. Frappat, P. P. Kulish, Э. Ragoucy, G. Rollet, “Temperley–Lieb $R$ -matrices from generalized Hadamard matrices”, Theoret. and Math. Phys., 178:2 (2014), 223–238
J. Avan, P. P. Kulish, G. Rollet, “Reflection matrices from Hadamard-type Temperley–Lieb $R$ -matrices”, Theoret. and Math. Phys., 179:1 (2014), 387–394
Ribeiro G.A.P., Lima-Santos A., “Bethe Ansatz for the Temperley-Lieb Spin Chain with Integrable Open Boundaries”, J. Stat. Mech.-Theory Exp., 2013, P02035
Lima-Santos A., “Temperley-Lieb K-Matrices”, J. Stat. Mech.-Theory Exp., 2013, P10021
Jean Avan, Baptiste Billaud, Geneviéve Rollet, “Classification of non-affine non-Hecke dynamical $R$ -matrices”, SIGMA, 8 (2012), 064, 45 pp.

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

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