Integrable Lattice Models for Conjugate $A^{(1)}_n$

TL;DR

This paper introduces a new class of integrable lattice models based on $A^{(1)}_n$ conjugate modular invariants, with weights parameterized by elliptic functions, satisfying the Yang-Baxter equation, and connecting to conformal field theories.

Contribution

The paper constructs novel $A^{(1)}_n$ integrable lattice models using nimrep graphs and elliptic weights, expanding the understanding of integrable systems and their continuum limits.

Findings

Models satisfy Yang-Baxter equation for all elliptic parameters.

At q=0, models realize representations of the Hecke algebra.

Models are linked to coset conformal field theories.

Abstract

A new class of $A^{(1)}_n$ integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the $A^{(1)}_n$ conjugate modular invariants, there being a model for each value of the rank and level. The Boltzmann weights are parameterized by elliptic theta functions and satisfy the Yang-Baxter equation for any fixed value of the elliptic nome q. At q=0, the models provide representations of the Hecke algebra and are expected to lead in the continuum limit to coset conformal field theories related to the $A^{(1)}_n$ conjugate modular invariants.