Polynominal Bases and Isoscalar Factors for SU(3)

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Abstract
The generators of SU(3) are represented by differential operators which act on states represented by functions of six independent variables. Orthonormal bases for irreducible representations are presented in the form of polynomials. These are used to construct bases for product representations, to derive the Clebsch‐Gordan series, and to find explicit expressions for certain special isoscalar factors. The general isoscalar factors are then expressed as sums over products of these special ones. Also, two types of recursion relation are derived for the general isoscalar factors; we illustrate our method of deriving these by deriving recursion relations for SU(2) which have been obtained recently by other means.