Internal labelling problem: an algorithmic procedure

Abstract

Combining the decomposition of Casimir operators induced by the embedding of a subalgebra into a semisimple Lie algebra with the properties of commutators of subgroup scalars, an analytical algorithm for the computation of missing label operators with the commutativity requirement is proposed. Two new criteria for subgroups scalars to commute are given. The algorithm is completed with a recursive method to construct orthonormal bases of states. As examples to illustrate the procedure, four labelling problems are explicitly studied.