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arXiv · 2112.09736

The $SU(3)\supset SO(3)$ missing label problem and the analytical Bethe ansatz

Nicolas Crampe·Dounia Shaaban Kabakibo·Luc Vinet
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Abstract

The missing label for basis vectors of $SU(3)$ representations corresponding to the reduction $SU(3) \supset SO(3)$ can be provided by the eigenvalues of $SO(3)$ scalars in the enveloping algebra of $su(3)$. There are only two such independent elements of degree three and four. It is shown how the one of degree four can be diagonalized using the analytical Bethe ansatz.

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Nicolas Crampe, Dounia Shaaban Kabakibo, Luc Vinet. 2021-12-17. The $SU(3)\supset SO(3)$ missing label problem and the analytical Bethe ansatz. https://doi.org/10.1142/s0217751x22500385

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