A new presentation for Specht modules with distinct parts

TL;DR

This paper introduces a novel presentation for Specht modules with conjugate shapes having strictly decreasing parts, using a linear operator on column tabloids, extending previous work on staircase shapes.

Contribution

It provides a new, simplified presentation for certain Specht modules, reducing the Garnir relations needed and generalizing earlier results on staircase shapes.

Findings

New linear operator on column tabloids introduced

Simplified presentation with fewer relations

Extended results to broader class of shapes

Abstract

We obtain a new presentation for Specht modules whose conjugate shapes have strictly decreasing parts by introducing a linear operator on the space generated by column tabloids. The generators of the presentation are column tabloids and the relations form a proper subset of the Garnir relations of Fulton. The results in this paper extend earlier results of the authors and Stanley on Specht modules of staircase shape.