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The structure of irreducible representations of (restricted) U_q(sl(3)) atroots of unity is understood within the Gelfand--Zetlin basis. The latter needsa weakened definition for non integrable representations, where the quadraticCasimir operator of the quantum subalgebra U_q(sl(2)) of U_q(sl(3)) is notcompletely diagonalized. This is necessary in order to take in account theindecomposable U_q(sl(2))-modules that appear. The set of redefined (mixed)states has a teepee shape inside the pyramid made with the wholerepresentation.

Non-integrable representations of the restricted quantum analogue ofsl(3)