Three blocks solvable lattice models and Birman–Murakami–Wenzl algebra
Vladimir Belavin (Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot, Israel, I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Moscow, Russia, Department of Quantum Physics, Institute for Information Transmission Problems, Moscow, Russia); Doron Gepner (Department of Particle Physics and Astrophysics, Weizmann Institute, Rehovot, Israel)
Birman–Murakami–Wenzl (BMW) algebra was introduced in connection with knot theory. We treat here interaction round the face solvable (IRF) lattice models. We assume that the face transfer matrix obeys a cubic polynomial equation, which is called the three block case. We prove that the three block theories all obey the BMW algebra. We exemplify this result by treating in detail the fused models, and showing explicitly the BMW structure. We use the connection between the construction of solvable lattice models and conformal field theory. This result is important to the solution of IRF lattice models and the development of new models, as well as to knot theory.
