New approach in theory of Clebsch-Gordan coefficients for u(n) and Uq(u(n))
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.
Publication Source (Journal or Book title)
Czechoslovak Journal of Physics
Tolstoy, V., & Draayer, J. (2000). New approach in theory of Clebsch-Gordan coefficients for u(n) and Uq(u(n)). Czechoslovak Journal of Physics, 50 (11), 1359-1369. https://doi.org/10.1023/A:1022846015548