On the algebraic approach to solvable lattice models

Vladimir Belavin, Doron Gepner

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Article number33
JournalJournal of High Energy Physics
Issue number2
StatePublished - 1 Feb 2019
Externally publishedYes


  • Conformal Field Theory
  • Integrable Field Theories
  • Lattice Integrable Models


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