论文标题
5-CB代数和Fused $ SU（2）$晶格型号
The 5-CB Algebra and Fused $SU(2)$ Lattice Models
论文作者
论文摘要
我们研究了Date等人提出的融合$ SU（2）$模型，这些模型是一系列具有任意块数量的模型，这是Boltzmann权重遵守的多项式方程的程度。我们通过直接计算证明，BMW（Birman-Murakami-Wenzl）代数的版本被五个，六个和七个块模型遵守，认为它是对具有两个以上块的任何模型有效的代数的一部分。为了建立这种猜想，我们假设某个ANSATZ具有模型的赋予性。我们使用杨 - 巴克斯特方程来明确描述五个区块的代数，获得了$ 19 $的额外非平淡关系。我们命名这个代数5--CB（保形编织）代数。我们的方法可用于描述此类可解决模型和任何数量块的任何可解决模型的代数。
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 BMW (Birman--Murakami--Wenzl) algebra is obeyed by five, six and seven blocks models, conjecturing that it is 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.
