Clebsch-Gordan coefficients of SU(3) in SU(2) and SO(3) bases

New algorithms are developed for the purpose of optimizing the efficient calculation of SU(3) Clebsch-Gordan coefficients in both SU(2)- and SO(3)-coupled bases. The new algorithms make use of the fact that highest weight states in a tensor product space are easily identified by vector coherent state methods. The methods are developed for SU(3) but apply to other compact semi-simple Lie groups. (C) 2000 American Institute of Physics. [S0022-2488(00)00109-2].