Polynomial Induction and the Restriction Problem

Abstract

We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This construction leads to a representation-theoretic proof of Littlewood's plethystic formula for the multiplicity of an irreducible representation of the symmetric group in such a restriction. The unimodality of certain bipartite partition functions follows.

11 pages

References in corpus (3)

• Specht modules decompose as alternating sums of restrictions of Schur modules
• Character Polynomials and the Restriction Problem
• Representations of monomial matrices and restriction from $G{L}_n$ to $S_n$

Cited by in corpus (1)

• Character Polynomials and the Restriction Problem