Pasquier Models at c=1: Cylinder Partition Functions and the role of the Affine Coxeter Element

Abstract

We calculate the partition functions of the affine Pasquier models on the cylinder in the continuum limit. We show that the partition function of any affine model may be expressed in terms of the orbit structure of the affine Coxeter element of the Weyl group associated with the defining graph of the model. Some of the consequences of this geometric relationship are explored.