Calculation of Clebsch-Gordan and Recah coefficients using symbolic manipulation programs (Q1123298)

Clebsch-Gordan and Racah coefficients can be thought of as special functions related to group representations. These coefficients arise from the decomposition of n-fold tensor products of the U(N) groups. The authors want to give procedures to a computer for calculating these coefficients rather than looking from their closed-form expression. Basic states are realized as polynomials in a space equipped with a differentiation inner product. The desired coefficients are then obtained by symbolically differentiating the relevant polynomials. Examples for SU(2) and SU(3) are given.