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

Abstract

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.