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

TL;DR

This paper computes the cylinder partition functions of affine Pasquier models in the continuum limit, revealing a geometric relationship with the affine Coxeter element's orbit structure in the Weyl group.

Contribution

It introduces a novel geometric approach linking affine model partition functions to the orbit structure of affine Coxeter elements.

Findings

Partition functions expressed via affine Coxeter element orbits

Geometric relationship between models and Weyl group structure

Implications for understanding affine model symmetries

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.