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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 179, Number 1, Pages 3–12
DOI: https://doi.org/10.4213/tmf8609 (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
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DOI: https://doi.org/10.4213/tmf8609
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.
Received: 07.11.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 179, Issue 1, Pages 387–394
DOI: https://doi.org/10.1007/s11232-014-0150-5
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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