A Note on the Decomposition Structure of the Direct Product of Irreducible Representations of SU(3) by Tensor Method
Open Access
- 1 July 1965
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 34 (1) , 46-55
- https://doi.org/10.1143/PTP.34.46
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' ≥λ+µ), it is shown that all the representations (α, β) are given by the following unique correspondence: For each pair of Iz, Y values (i.e., to each `weight') occurring in the representation (λ, µ) we have a representation (α, β) with α=λ'+Iz+(3/2)Y, β=µ'+Iz-(3/2)Y, where the multiplicity of occurrence of (α, β) is the same as the multiplicity of the weight Iz, Y in the representation (λ, µ).Keywords
This publication has 1 reference indexed in Scilit:
- On the multiplicity of an irreducible representation in a direct product of irreducible representations of SU (3)Il Nuovo Cimento (1869-1876), 1963