Two-body homogeneous rational Gaudin models and the missing label problem

Abstract

For the N = 2 rational Gaudin Hamiltonians based on , it is shown that the spectral invariants of the Lax matrix correspond to linear combinations of the labelling operators associated with the embedding of Lie algebras . The diagonalized spectral invariants are applied to the degeneracy separation in the Clebsch–Gordan series of .