  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.
