NONINTEGRABLE REPRESENTATIONS OF THE RESTRICTED QUANTUM ANALOG OF SL(3)

The structure of irreducible representations of (restricted) U-q(sl(3) ) at roots of unity is understood within the Gelfand-Zetlin basis. The latter needs a weakened definition for nonintegrable representations, where the quadratic Casimir operator of the quantum subalgebra U-q(sl (2)) subset of U-q(sl(3)) is not completely diagonalized. This is nece ssary in order to take into account the indecomposable U-q(sl(2))-modu les that appear. The set of redefined (mixed) states has a teepee shap e inside the pyramid made with the whole representation.