Plethysm

In algebra, plethysm is an operation on symmetric functions introduced by Dudley E. Littlewood,[1] who denoted it by {λ} ⊗ {μ}.

Let V be a vector space over the complex numbers, considered as a representation of the general linear group GL(V).

Each Young diagram λ corresponds to a Schur functor Lλ(-) on the category of GL(V)-representations.

Given two Young diagrams λ and μ, consider the decomposition of Lλ(Lμ(V)) into a direct sum of irreducible representations of the group.

The character of the GL(V)-representation Lλ(V) is a symmetric function in dim(V) variables, known as the Schur polynomial sλ corresponding to the Young diagram λ. Schur polynomials form a basis in the space of symmetric functions.