Discrete parafermions are the lattice analog of conserved currents in a Quantum Field Theory, and are used in the Probability literature as a central tool for the rigorous study of statistical models in the scaling limit. It was realised recently that they arise from the Hopf algebra symmetry underlying critical integrable lattice models. In this talk, I will extend these ideas to an integrable lattice model in which the Hopf algebra symmetry is preserved out of criticality: the chiral Potts model. I will first review the Bernard-Felder construction of lattice conserved currents on one hand, and the basic physics and algebraic structure of the chiral Potts model on the other hand. Then, using these ingredients, I will describe the discrete parafermions in this model, and give the interpretation of their conservation equations in terms of perturbed Conformal Field Theory. Joint work with Robert Weston (Herriot-Watt, Edimbourg)

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