Abstract
The construction of integrity bases and invariant operators for the finite subgroups of SO3 is outlined. The integrity bases are realized in terms of rotationally invariant sets of kets and the invariant operators in terms of irreducible tensorial sets. A building-up principle is developed for integrity bases and invariant operators and the latter used to complete the state labelling for the non-canonical subgroup chains. The invariant operators are applied to the symmetry adaptation of Gel'fand states and to the study of coupling and transformation coefficients.
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