ABSTRACT
This chapter discusses Young tableaux in connection with the irreducible representations of the symmetric groups. It shows that they are useful for dealing with irreducible representations of Lie groups. Young tableaux correspond to irreducible representations of the permutation group, and the connection with the irreducible representations of SU(3) is that the irreducible representations of SU(3) transform irreducibly under permutation of the labels of the indices. A Young tableau is a rule for symmetrizing a tensor to project out a specific irreducible representation. In SU(3), the tensors corresponding to Young tableaux with more than three boxes in any column vanish because no tensor can be completely antisymmetric in four or more indices which take on only three values.
