Partition Functions, Intertwiners and the Coxeter Element

TL;DR

This paper explores the geometric structure of partition functions and intertwiners in Pasquier models, revealing their positivity and connections to SU(2) subgroups, and suggesting broader geometric frameworks for these models.

Contribution

It reinterprets earlier results on intertwiners in Pasquier models geometrically, establishing their positivity and linking them to finite SU(2) subgroups.

Findings

Positivity of intertwiners established generally

Connections made between intertwiners and SU(2) subgroups

Geometrical interpretation of partition functions

Abstract

The partition functions of Pasquier models on the cylinder, and the associated intertwiners, are considered. It is shown that earlier results due to Saleur and Bauer can be rephrased in a geometrical way, reminiscent of formulae found in certain purely elastic scattering theories. This establishes the positivity of these intertwiners in a general way and elucidates connections between these objects and the finite subgroups of SU(2). It also offers the hope that analogous geometrical structures might lie behind the so-far mysterious results found by Di Francesco and Zuber in their search for generalisations of these models.