J. Avan, T. Fonseca, L. Frappat, P. P. Kulish, Э. Ragoucy, G. Rollet, “Temperley–Lieb <nobr>$R$</nobr>-matrices from generalized Hadamard matrices”, TMF, 2014, Volume 178, Number 2,Pages <nobr>255

This article is cited in 7 papers

Temperley–Lieb $R$-matrices from generalized Hadamard matrices

J. Avan^a, T. Fonseca^b, L. Frappat^b, P. P. Kulish^c, Э. Ragoucy^ab, G. Rollet^a

^a Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, Cergy-Pontoise, France
^b Laboratoire d'Annecy-le-Vieux de Physique Théorique, CNRS — Université de Savoie, Annecy-le-Vieux, France
^c St. Petersburg Department of the~Steklov Institute of Mathematics, St. Petersburg, Russia

Abstract: We construct new sets of rank $n$-representations of the Temperley–Lieb algebra $TL_N(q)$ that are characterized by two matrices with a generalized complex Hadamard property. We give partial classifications for the two matrices, in particular, in the case where they reduce to Fourier or Butson matrices.

Keywords: Yang–Baxter equation, Temperley–Lieb algebra, $R$-matrix, Hadamard matrix.

Received: 18.06.2013

DOI: 10.4213/tmf8564