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TMF, 2014, Volume 179, Number 1, Pages 3–12 (Mi tmf8609)  

This article is cited in 1 scientific paper (total in 2 paper)

Reflection matrices from Hadamard-type Temperley–Lieb $R$-matrices

J. Avana, P. P. Kulishb, G. Rolleta

a Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, Cergy-Pontoise, France
b St. Petersburg Department of the Steklov Institute of Mathematics, St. Petersburg, Russia

Abstract: We classify nonoperatorial matrices $K$ solving the Skylanin quantum reflection equation for all $R$-matrices obtained from the newly defined general rank-$n$ Hadamard-type representations of the Temperley–Lieb algebra $TL_N(\sqrt{n})$. They are characterized by a universal set of algebraic equations in a specific canonical basis uniquely defined by the “master matrix” associated with the chosen realization of the Temperley–Lieb algebra.

Keywords: reflection equation, Yang–Baxter equation, Temperley–Lieb algebra

DOI: https://doi.org/10.4213/tmf8609

Full text: PDF file (382 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 179:1, 387–394

Bibliographic databases:

Received: 07.11.2013

Citation: J. Avan, P. P. Kulish, G. Rollet, “Reflection matrices from Hadamard-type Temperley–Lieb $R$-matrices”, TMF, 179:1 (2014), 3–12; Theoret. and Math. Phys., 179:1 (2014), 387–394

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. “Osnovnye nauchnye trudy Petra Petrovicha Kulisha”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 23, Zap. nauchn. sem. POMI, 433, POMI, SPb., 2015, 8–19  mathnet  mathscinet
    2. N. Kitanine, R. I. Nepomechie, N. Reshetikhin, “Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish”, J. Phys. A-Math. Theor., 51:11 (2018), 110201  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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