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

Behrend, Roger E.; Evans, David E.

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

Authors

Description

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