This article is cited in 1 paper

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

J. Avan^a, P. P. Kulish^b, G. Rollet<sup>a

a</sup> 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.

Received: 07.11.2013

DOI: 10.4213/tmf8609

 English version: Theoretical and Mathematical Physics, 2014, 179:1, 387–394

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