Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série STR-LPT-ENS-HE
Domaines hep-th
Date Mardi 16 Octobre 2018
Heure 11:35
Institut LPTENS
Salle LPTENS library
Nom de l'orateur Gepner
Prenom de l'orateur Doron
Addresse email de l'orateur
Institution de l'orateur Weizmann
Titre Three block solvable lattice models and Birman-Murakami-Wenzl algebra
Résumé We treat in this talk 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, but we still do not know all the relations of this algebra. The four blocks result, that is the BMW algebra and the four blocks Skein relation, is enough to define new knot polynomials, important in knot theory.
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