Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1
- Authors
- Type
- Published Article
- Publication Date
- Feb 27, 1997
- Submission Date
- Oct 22, 1996
- Identifiers
- DOI: 10.1088/0305-4470/30/10/027
- arXiv ID: q-alg/9610025
- Source
- arXiv
- License
- Unknown
- External links
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.