2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184321A 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 footnoteHigh Energy Physics - TheoryStatistical MechanicsMathematical PhysicsExactly Solvable and Integrable Systemstext