Polynomial irreducible tensors for point groups

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Abstract
Generating functions for (Γr,Γm) tensors for any point group G and any pair of its irreducible representations Γr and Γm are calculated explicitly. A (Γr,Γm) tensor transforms according to Γr, and its components are polynomials in another tensor transforming by Γm. Explicit integrity bases of (Γr,Γm) tensors are given for all pairs Γr and Γm for the groups Cn, Dn, T, and O, and for the same groups with reflections. A composition rule for extending the result to reducible representations is formulated. Point group tensors irreducible with respect to SO(3) are obtained, together with their generating functions.

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