Internal-Labeling Problem

Abstract
A method is proposed for labeling the bases of a compact group when reduced with respect to an arbitrary subgroup. The scheme is based on the observation that the heaviest state of a multiplet (subgroup irreducible representation) of an IR (group irreducible representation) can be labeled by a product of heaviest states of simpler ``elementary'' multiplets. Details are worked out for a number of group‐subgroup combinations.