Characteristic-free resolutions of Weyl and Specht modules

TL;DR

This paper constructs explicit resolutions for Weyl and co-Specht modules, providing new tools for understanding their structure and proving a conjecture related to their resolutions.

Contribution

It introduces characteristic-free resolutions of Weyl and co-Specht modules and confirms a conjecture by Boltje-Hartmann on co-Specht module resolutions.

Findings

Resolutions of Weyl modules by divided powers

Resolutions of co-Specht modules by permutational modules

Proof of Boltje-Hartmann conjecture

Abstract

We construct explicit resolutions of Weyl modules by divided powers and of co-Specht modules by permutational modules. We also prove a conjecture of Boltje-Hartmann on resolutions of co-Specht modules.