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

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.

References in corpus (3)

• Bethe eigenvectors of higher transfer matrices
• Internal labelling operators and contractions of Lie algebras
• Resolution of the GL(3) - O(3) state labelling problem via O(3)-invariant Bethe subalgebra of the twisted Yangian