The external labelling problem and Clebsch-Gordan series of semisimple Lie algebras

摘要

It is shown that the external labelling problem s subset of s circle plus s for simple Lie algebras can be solved in a satisfactory manner taking into account the decomposability properties of the Casimir operators of s circle plus s. This enables us to construct a complete set of commuting labelling operators for irreducible representations of s circle plus s, allowing us in particular to separate the degeneracies in the Clebsch-Gordan series of the simple Lie algebra s.