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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 178, Number 2, Pages 255–273
DOI: https://doi.org/10.4213/tmf8564 (Mi tmf8564) 		 
This article is cited in 7 scientific papers (total in 8 papers)

Temperley–Lieb R-matrices from generalized Hadamard matrices

J. Avana, T. Fonsecab, L. Frappatb, P. P. Kulishc, Э. Ragoucyab, G. Rolleta

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
Full-text PDF (539 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf8564
Abstract: We construct new sets of rank n-representations of the Temperley–Lieb algebra TLN(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
English version:
Theoretical and Mathematical Physics, 2014, Volume 178, Issue 2, Pages 223–238
DOI: https://doi.org/10.1007/s11232-014-0138-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: J. Avan, T. Fonseca, L. Frappat, P. P. Kulish, Э. Ragoucy, G. Rollet, “Temperley–Lieb R-matrices from generalized Hadamard matrices”, TMF, 178:2 (2014), 255–273; Theoret. and Math. Phys., 178:2 (2014), 223–238
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    1. Bytsko A., “A Relation For the Jones-Wenzl Projector and Tensor Space Representations of the Temperley-Lieb Algebra”, Linear Multilinear Algebra, 68:11 (2020), 2239–2253  crossref  mathscinet  isi
    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
    3. T. Banica, “Complex Hadamard matrices with noncommutative entries”, Ann. Funct. Anal., 9:3 (2018), 354–368  crossref  mathscinet  isi  scopus
    4. T. Banica, D. Ozteke, L. Pittau, “Isolated partial Hadamard matrices and related topics”, Open Syst. Inf. Dyn., 25:2 (2018), 1850009  crossref  mathscinet  isi  scopus
    5. “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
    6. Bytsko A., “Tensor Space Representations of Temperley-Lieb Algebra Via Orthogonal Projections of Rank R >= 1”, J. Math. Phys., 56:8 (2015), 083502  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Bytsko A., “Tensor Space Representations of Temperley-Lieb Algebra and Generalized Permutation Matrices”, J. Math. Phys., 56:8 (2015), 083503  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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