We describe the Boltzmann weights of the $D_k$ algebra spin vertex models. Thus, we find the $SO(N)$ spin vertex models, for any N, completing the $B_k$ case found earlier. We further check that the real (self–dual) SO(N) models obey quantum algebras, which are the Birman–Murakami–Wenzl (BMW) algebra for three blocks, and certain generalizations, which include the BMW algebra as a sub–algebra, for four and five blocks. In the case of five blocks, the $B_4$ model is shown to satisfy additional twenty new relations, which are given. The $D_6$ model is shown to obey two additional relations.

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关于SO（N）自旋顶点模型

我们描述了 $d_{ķ}$代数自旋顶点模型。因此，我们发现$\mathrm{小号}Ø（ñ）$自旋顶点模型，对于任何N，完成${乙}_{ķ}$案发现较早。我们进一步检查实数（自对偶）SO（N）模型遵循量子代数，即三个块的Birman-Murakami-Wenzl（BMW）代数，以及某些概括，包括BMW代数作为子代数，适用于四个和五个街区。如果是五个街区，${乙}_4$模型显示满足另外20个新关系，并给出了这些关系。的$d_6$ 模型显示服从另外两个关系。