Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series STR-LPT-ENS-HE
Subjects hep-th
Date Tuesday 16 October 2018
Time 11:35
Institute LPTENS
Seminar Room LPTENS library
Speaker's Last Name Gepner
Speaker's First Name Doron
Speaker's Email Address
Speaker's Institution Weizmann
Title Three block solvable lattice models and Birman-Murakami-Wenzl algebra
Abstract 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.
arXiv Preprint Number

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