Status  Confirmed 
Seminar Series  STRLPTENSHE 
Subjects  hepth 
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 BirmanMurakamiWenzl 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 BirmanMurakamiWenzl (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 subalgebra 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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