The construction of a class of presentations for Specht modules

TL;DR

This paper develops new classes of presentations for Specht modules using a linear operator based on dual Garnir relations, applicable to most shapes of these modules.

Contribution

It introduces a novel construction method for Specht module presentations leveraging symmetrized dual Garnir relations, expanding existing frameworks.

Findings

New presentations for most Specht module shapes

Linear operator based on dual Garnir relations

Applicable to a broad class of Specht modules

Abstract

We build on the methods introduced by Friedmann, Hanlon, Stanley, and Wachs, and further developed by Brauner and Friedmann, to construct additional classes of presentations of Specht modules. We obtain these presentations by defining a linear operator which is a symmetrized sum of dual Garnir relations on the space of column tabloids. Our presentations apply to the vast majority of shapes of Specht modules.