On McKay's propagation theorem for the Foulkes conjecture

TL;DR

This paper reinterprets McKay's propagation theorem for the Foulkes conjecture using weight spaces and tensor invariants, simplifying its proof and providing clearer insight into the theorem.

Contribution

It offers a new, more elegant proof of McKay's propagation theorem by translating it into the language of weight spaces and tensor invariants.

Findings

Simplified proof of McKay's propagation theorem

New interpretation using weight spaces and tensor invariants

Enhanced understanding of the Foulkes conjecture

Abstract

We translate the main theorem in Tom McKay's paper "On plethysm conjectures of Stanley and Foulkes" (J. Alg. 319, 2008, pp. 2050-2071) to the language of weight spaces and projections onto invariant spaces of tensors, which makes its proof short and elegant.