The 5-CB algebra and fused SU(2) lattice models

We study the fused SU(2) models put forward by Date et al, that are a series of models with arbitrary number of blocks, which is the degree of the polynomial equation obeyed by the Boltzmann weights. We demonstrate by a direct calculation that a version of Birman-Murakami-Wenzl (BMW) algebra [1, 2] is obeyed by five, six and seven blocks models, conjecturing that the BMW algebra is a part of the algebra valid for any model with more than two blocks. To establish this conjecture, we assume that a certain ansatz holds for the baxterization of the models. We use the Yang-Baxter equation to describe explicitly the algebra for five blocks, obtaining 19 additional non-trivial relations. We name this algebra 5-CB (conformal braiding) algebra. Our method can be utilized to describe the algebra for any solvable model of this type and for any number of blocks.