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)) (Q1090781)

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.