New approach in theory of Clebsch-Gordan coefficients for u(n) and Uq(u(n))

V. N. Tolstoy, Lomonosov Moscow State University
J. P. Draayer, Louisiana State University


A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebra u(n) and its quantum analog Uq(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebra u(n-1) (Uq(u(n-1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator of u(n) and Uq(u(n)). It is shown that the Uq(u(n)) CGCs can be presented in terms of the Uq(u(n-1)) q-9j-symbols.