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

Abstract

A new class of $A_n^{(1)}$ integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the $A_n^{(1)}$ 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 $A_n^{(1)}$ conjugate modular invariants.

18 pages. v2: minor changes, such as page 11 footnote