A necessary and sufficient condition for the existence of real coupling coefficients for a finite group | Zendy

Bickerstaff R. P. | Zendy; Damhus T. | Zendy

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A necessary and sufficient condition for the existence of real coupling coefficients for a finite group

Author(s) -

Bickerstaff R. P.,

Damhus T.

Publication year - 1985

Publication title -

international journal of quantum chemistry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.484

H-Index - 105

eISSN - 1097-461X

pISSN - 0020-7608

DOI - 10.1002/qua.560270403

Subject(s) - group (periodic table) , isomorphism (crystallography) , coupling (piping) , mathematics , set (abstract data type) , point (geometry) , matrix (chemical analysis) , finite group , pure mathematics , group theory , physics , quantum mechanics , computer science , geometry , chemistry , materials science , crystallography , chromatography , crystal structure , programming language , metallurgy

We establish a theorem which gives a necessary and sufficient condition for a set of matrix irreps of a finite group to admit real coupling (Clebsch–Gordan) coefficients. The proof is based on the method used by Feit to prove that a full set of coupling coefficients for a finite group determines the group up to isomorphism. A consequence of the theorem is that a finite group with real coupling coefficients is necessarily quasiambivalent . The theorem is used to demonstrate that real coupling coefficients do not exist for the point‐group hierarchies T ⊃ D 2 and I ⊃ T or for the double‐group hierarchies I * ⊃ D 3 *, I * ⊃ D 5 *, and O * ⊃ D 3 *.

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