We construct new solvable vertex models based on the spin representation of the Lie algebra $B_k$. We use these models to study the algebraic structure underlying such vertex theories. We show that all the $B_k$ spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebras were discussed before for various IRF (interaction round the face) models. Here we establish that the same algebras hold for vertex models.

中文翻译：

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B _k自旋顶点模型和量子代数

我们基于李代数的自旋表示构造新的可解顶点模型 ${乙}_{ķ}$。我们使用这些模型来研究这些顶点理论所基于的代数结构。我们证明所有${乙}_{ķ}$自旋顶点模型遵循BMW代数的形式以及称为n –CB（共形编织）代数的额外关系。这些代数在前面针对各种IRF（面对面交互）模型进行了讨论。在这里，我们建立相同的代数适用于顶点模型。