On the $D_n$ Spin Vertex Models for Odd $n$

Solvable vertex models in two dimensions are of importance in conformal field theory, phase transitions and integrable models. We consider here the $D_n$ spin vertex models, for $n$ which is odd. The models involve also the anti–spinor representation. We describe here the Boltzmann weights for these representations using crossing symmetry from the previously known spinor representations. For calculation reasons we limit ourself to the $n=3$ and $n=5$ cases, which are described explicitly.