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 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. (C) 2020 The Author(s). Published by Elsevier B.V.