Integrable lattice models for conjugate An(1)

A new class of A(n)((1)) integrable lattice models is presented. These are interactionround-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 parametrized 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.