Abstract
Irreducible representations of \(\mathcal{U}_q (sl(3))\) at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra \(\mathcal{U}_q (sl(2)) \subset \mathcal{U}_q (sl(3))\) not to be completely diagonalised. Some irreducible representations of \(\mathcal{U}_q (sl(3))\) indeed contain indecomposable \(\mathcal{U}_q (sl(2))\)-modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation.
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Arnaudon, D. Representations of \(\mathcal{U}_q (sl(3))\) at roots of 1 (In the restricted specialisation). Czechoslovak Journal of Physics 47, 1075–1082 (1997). https://doi.org/10.1023/A:1021693730271
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DOI: https://doi.org/10.1023/A:1021693730271