The 4-CB algebra and solvable lattice models
Vladimir Belavin (Department of Quantum Physics, Institute for Information Transmission Problems, Bolshoy Karetny per. 19, Moscow, 127994, Russia, Physics Department, Ariel University, Ariel, 40700, Israel, I.E. Tamm Department of Theoretical Physics, P.N Lebedev Physical Institute, Leninsky av. 53, Moscow, 11991, Russia); Doron Gepner (Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot, 76100, Israel); Jian-Rong Li (Institute of Mathematics and Scientific Computing, University of Graz, Graz, 8010, Austria); Ran Tessler (Department of Mathematics, Weizmann Institute, Rehovot, 76100, Israel)
We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the number of blocks, which is the degree of polynomial equation obeyed by the Boltzmann weights. Using the Yang-Baxter equation and the ansatz for the Baxterization of the models, we show that the three blocks models obey a version of Birman-MurakamiWenzl (BMW) algebra. For four blocks, we conjecture that the algebra, which is termed 4-CB (Conformal Braiding) algebra, is the BMW algebra with a different skein relation, along with one additional relation, and we provide evidence for this conjecture. We connect these algebras to knot theory by conjecturing new link invariants. The link invariants, in the case of four blocks, depend on three arbitrary parameters. We check our result for G 2 model with the seven dimensional representation and for SU(2) with the isospin 3/2 representation, which are both four blocks theories.
