Direct use of Young tableau algebra to generate the Clebsch–Gordan coefficients of S U (2)

Although it is well known that the irreducible representations of the SU (N) groups may be generated by using Young tableau algebra, this technique seems to have found little use for the derivation of closed algebraic expressions for the Clebsch–Gordan coefficients of these groups. A frontal attack on the derivation of these coefficients using tableau symmetrizers is described. As an example, the SU (2) group illustrates the fundamental ideas behind the process.