Non integrable representations of the restricted quantum analogue of   sl(3) at roots of 1
  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 non integrable representations, where the quadratic Casimir operator of the quantum subalgebra U_q(sl(2)) of U_q(sl(3)) is not completely diagonalized. This is necessary in order to take in account the indecomposable U_q(sl(2))-modules that appear. The set of redefined (mixed) states has a teepee shape inside the pyramid made with the whole representation. 
Daniel Arnaudon