Journal of High Energy Physics

, 2019:33 | Cite as

On the algebraic approach to solvable lattice models

  • Vladimir Belavin
  • Doron GepnerEmail author
Open Access
Regular Article - Theoretical Physics


We treat here interaction round the face (IRF) solvable lattice models. We study the algebraic structures underlining such models. For the three block case, we show that the Yang Baxter equation is obeyed, if and only if, the Birman-Murakami-Wenzl (BMW) algebra is obeyed. We prove this by an algebraic expansion of the Yang Baxter equation (YBE). For four blocks IRF models, we show that the BMW algebra is also obeyed, apart from the skein relation, which is different. This indicates that the BMW algebra is a sub-algebra for all models with three or more blocks. We find additional relations for the four block algebra using the expansion of the YBE. The four blocks result, that is the BMW algebra and the four blocks skein relation, is enough to define new knot invariant, which depends on three arbitrary parameters, important in knot theory.


Conformal Field Theory Integrable Field Theories Lattice Integrable Models 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsWeizmann InstituteRehovotIsrael
  2. 2.I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical InstituteMoscowRussia
  3. 3.Department of Quantum PhysicsInstitute for Information Transmission ProblemsMoscowRussia

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