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Zur Berechnung der Clebsch-Gordan-Koeffizienten halbeinfacher Liescher Gruppen. II: Die Berechnung der Clebsch-Gordan-Koeffizienten der SU(3). (On the calculation of Clebsch-Gordan coefficients of semisimple Lie groups. II: The calculation of the Clebsch-Gordan coefficients of SU(3)). (German) Zbl 0622.22010

The general approach to the calculation of the Clebsch-Gordan coefficients in the theory of semisimple Lie groups developed in a previous paper by the author [ibid. 24, 29-40 (1987; Zbl 0617.22018)] is applied to the case of the SU(3) group. In the Gel’fand-Zeitlin notations the generation procedure for the canonical basis as well as the choice of the highest weight vectors are described in detail. A new formula for the multiplicity of appearance of irreducible representations of SU(3) in the Clebsch-Gordan expansion of a direct product of representations is obtained.
Reviewer: A.Bogush

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
22E46 Semisimple Lie groups and their representations
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
22-04 Software, source code, etc. for problems pertaining to topological groups

Citations:

Zbl 0617.22018
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