Periodic and flat irreducible representations ofSU(3) q

We construct all the periodic irreducible representations ofU(SU(3)) _q forq am-root of unity. Their dimensions arek(2m) ² fork=1,...,m (onlyk=1,...,m/2 for evenm). Their interest is that they could be a tool to generalize the chiral Potts model. By truncation of these representations, we construct flat representations ofU(SU(3)) _q , in which all the multiplicities of the weights are set to 1.