Circular matrices, duality theorems and the reality of Clebsch-Gordan coefficients (Q1071116)
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scientific article; zbMATH DE number 3937439
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Circular matrices, duality theorems and the reality of Clebsch-Gordan coefficients |
scientific article; zbMATH DE number 3937439 |
Statements
Circular matrices, duality theorems and the reality of Clebsch-Gordan coefficients (English)
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1985
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A necessary and sufficient condition for the reality of the Clebsch-Gordan (CG) coefficients of a symmetry group is obtained. Attention is restricted to finite-dimensional irreducible representations. The relevance of the duality theorems of Pontryagin-van Kampen and of Tanaka-Krein to the criterion of reality of CG coefficients is demonstrated. It is also shown that a generalization of the Frobenius-Schur invariant can provide a sufficient condition for reality.
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circular matrices
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Clebsch-Gordan coefficients
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reality condition
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duality theorems
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