Abstract
Following a general exposition of the theory of 3-Γ symbols [1], we now focus on the particular features encountered when dealing with double groups of (proper as well as improper) point groups.
The paper starts with a brief outline of the definition of double groups adopted in the present work. After this, some properties of double group 3-Γ symbols are discussed which are independent of the way the 3-Γ symbols have been constructed. The main part of the paper then deals with the actual generation of 3-Γ symbols for the non-commutative double groups.
In the approach described, the 3-Γ symbols become determined in part by adaption of the standard matrix irreps to subgroup hierarchies and then completely, phases included, by the specification of standard basis functions (or, equivalently, standard subduction coefficients).
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Damhus, T., Harnung, S.E. & Schäffer, C.E. Phase-fixed double-group 3-Γ symbols. II. General features of double groups and their 3-Γ symbols. Theoret. Chim. Acta 65, 365–387 (1984). https://doi.org/10.1007/BF00550835
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DOI: https://doi.org/10.1007/BF00550835