Polynomial Induction and the Restriction Problem
Representation Theory
2021-12-17 v1 Combinatorics
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.
Cite
@article{arxiv.2004.03928,
title = {Polynomial Induction and the Restriction Problem},
author = {Sridhar P. Narayanan and Digjoy Paul and Amritanshu Prasad and Shraddha Srivastava},
journal= {arXiv preprint arXiv:2004.03928},
year = {2021}
}
Comments
11 pages