The construction of orthonormal bases of eigenstates for the missing label problem is considered, with special emphasis on the special case of reductions with respect to the Cart an subalgebra of a reductive Lie algebra, leading to the so-called Racah operators. Some general properties of this type of labelling operators are analyzed. For the unitary case, it is shown that Racah operators constructed from Casimir operators generally do not suffice to construct orthonormal bases of states for generic irreducible representations. Various examples of explicit constructions of orthonormal bases of states are given.
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