Representations of Uq(sl(3)) at roots of 1 (in the restricted specialisation)

Irreducible representations of Uq(sl(3)) at roots of unity in the restricted specialization are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra Uq(sl(2)) which is contained in Uq(sl(3)) not to be completely diagonalized. Some irreducible representations of Uq(sl(3)) indeed contain indecomposable Uq(sl(2))-modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation. (author)