ON FACTORIZATION OF THE NORMALIZATION SU(3) CLEBSCH-GORDAN-COEFFICIENTS

The use of the factorized form of the extremal projection operator for the U(3) algebra allows one to prove the factorization of normalizati on Clebsch-Gordan coefficients {(lambda(1), mu(1))H-1 circle times (la mbda(2), mu(2))H - H-1\(lambda mu)H}(H is the highest weight) into the product of three simple SU(2) normalization Clebsch-Gordan coefficien ts in multiplicity free cases. A similar conclusion is conjectured to be valid for arbitrary simple Lie algebras (superalgebras) and their q analogs.