Algebraic Tabulation of Clebsch-Gordan Coefficients of SU3 for the Product (λ, μ)⊗ (1, 1) of Representations of SU3

Abstract

An algebraic tabulation is made of the Clebsch‐Gordan (CG) coefficients of SU 3 which occur in the reduction into irreducible representations of the direct product (λ, μ) ⊗ (1, 1) of irreducible representations of SU 3. Full explanation is made of the method of handling the complications associated with the possible double occurrence of the representation (λ, μ) itself in the direct product. The phase convention employed is an explicitly stated generalization of the well‐known Condon and Shortley phase convention for SU 2. The relationship of the CG coefficients associated with the direct product (1, 1) ⊗ (λ, μ) to those coefficients already mentioned is also exhibited.