On SO$(N)$ spin vertex models

Vladimir Belavin; Doron Gepner; Hans Wenzl

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arXiv · 2007.15939

On SO$(N)$ spin vertex models

Vladimir Belavin·Doron Gepner·Hans Wenzl

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Abstract

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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Vladimir Belavin, Doron Gepner, Hans Wenzl. 2020-07-31. On SO$(N)$ spin vertex models. https://arxiv.org/abs/2007.15939

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