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Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1

Daniel Arnaudon
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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.

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Daniel Arnaudon. 1997-02-27. Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1. https://doi.org/10.1088/0305-4470%2F30%2F10%2F027

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