As has long been known, the irreducible tensor representations of GL(d) of rank n may be labeled by means of the irreducible representations of S n , i.e., by means of the Young diagrams [λ], where λ 1 + λ 2 + … λ r = n. We denote such a tensor representation by 〈λ〉. Using Young's raising operator R ij we can write [1, p. 42]

1.1

where the dot denotes the inducing process. For example, [3] . [2] is that representation of S 5 induced by the identity representation of its subgroup S 3 × S 2.