The Inner Plethysm of S-Functions
D. E. Littlewood · Canadian Journal of Mathematics · 1958
In a previous paper (2), the inner product of two S-functions {λ}.{μ} was defined for (λ),(μ) partitions of the same integer n. Briefly, the ordinary product {λ}.{μ} of two S-functions corresponds to the analysis of the direct product of two corresponding representations of the full linear group, while the inner product {λ}.{μ} corresponds to the analysis of the direct product of two representations of the corresponding symmetric group.