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

Abstract

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebrau(n−1) (U q(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 ofu(n) andU q(u(n)). It is shown that theU q(u(n)) CGCs can be presented in terms of theU q(u)(n−1)) q−9j-symbols.