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arXiv 2001.09280hep-thmath-phmath.MP
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5- CB代数与融合$SU(2)$格点模型

The 5-CB Algebra and Fused $SU(2)$ Lattice Models

Vladimir Belavin, Doron Gepner

备注：
20 pages, no figures, Mathematica notebook attached. Added references and corrected some erroneous 5--CB relations
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摘要：

我们研究了Date等人提出的融合$SU(2)$模型，这是一系列具有任意块数的模型，这是Boltzmann权重所服从的多项式方程的次数。我们证明了一个版本的宝马（Birman-Murakami--Wenzl）代数服从五，六，七块模型的直接计算，说明它是代数的一部分，有效的任何模型与两个以上的块。为了建立这个猜想，我们假设一个特定的假设对模型的baxterization成立。我们使用杨-巴克斯特方程来明确地描述五个块的代数，获得$19$额外的非平凡的关系。我们称这种代数为5--CB（Conformal Braiding）代数。我们的方法可以用来描述这种类型的任何可解模型和任何数量的块的代数。

英文摘要：

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.

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