Abstract
We present the projection operator method in combination with the Wigner-Racah calculus of the subalgebra U q(su(2)) for calculation of Clebsch-Gordan coefficients (CGCs) of the quantum algebra U q(su(3)). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form for the projection operator of U q(su(3)). We obtain a very compact general analytic formula for the U q(su(3)) CGCs in terms of the U q(su(2)) Wigner 3nj symbols.
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