Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1
Abstract
The structure of irreducible representations of (restricted) Uq(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 Uq(sl(2)) of Uq(sl(3)) is not completely diagonalized. This is necessary in order to take in account the indecomposable Uq(sl(2))-modules that appear. The set of redefined (mixed) states has a teepee shape inside the pyramid made with the whole representation.
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