A note on the decomposition structure of the direct product of irreducible representations of SU(3) by tensor method

Abstract

Tensor methods are employed to determine which unitary irreducible representations (UIR's) (α, β) occur in the reduction of the direct product (λ, μ)⊗(λ', μ') of two arbitrary UIR's of SU(3). For λ', μ' large enough (λ', μ' ≥α+β), it is shown that all the representations (α, β) are given by the following unique correspondence: For each pair of I_z, Y values (i.e., to each 'weight') occurring in the representation (λ, μ) we have a representation (α, β) with α=λ'+I_z+(3/2)Y, μ=μ'+I_z-(3/2)Y, where the multiplicity of occurrence of (α, β) is the same as the multiplicity of the weight I_z, Y in the representation (λ, μ).