Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1
arXiv:q-alg/9610025 · doi:10.1088/0305-4470/30/10/027
Abstract
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.
17 pages, LaTeX2e, uses epic.sty; some supplementary pictures are available at http://lapphp0.in2p3.fr/~arnaudon/teepee.html ; title changed, more details in the introduction, some references added; to appear in J. Phys. A: Math. Gen