On bases for irreducible representations of O (3) suitable for systems with an arbitrary finite symmetry group

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Abstract
The problem of constructing bases for representations of the rotation group O (3) adapted to an arbitrary discrete subgroup symmetry is considered. For each discrete subgroup Γ, we construct all Γ invariant operator valued functions of the generators of O (3). These invariant operators can be used to resolve the missing label problem in the O (3) ⊆Γ reduction and also to construct the corresponding bases functions.