On SO(N) spin vertex models

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 B₄ model is shown to satisfy additional twenty new relations, which are given. The D₆ model is shown to obey two additional relations.