Greene's Theorem and ideals of the group algebra of a symmetric group

TL;DR

This paper investigates algebraic structures related to symmetric groups, demonstrating bases for certain factor rings of their group algebra and identifying generators for annihilators of permutation modules.

Contribution

It introduces new bases for factor rings of the symmetric group's algebra and provides generators for specific annihilator modules, advancing understanding of their algebraic properties.

Findings

Certain factor rings have natural bases of group elements

Generators for annihilators of permutation modules are identified

Enhanced understanding of the algebraic structure of symmetric groups

Abstract

We show that certain factor rings of the group algebra of a symmetric group have natural bases of group elements. We also give generators for the annihilator of certain permutation modules for symmetric groups.