Some reducible Specht modules for Iwahori--Hecke algebras of type $A$ with $q=-1$

TL;DR

This paper proves the reducibility of a large class of Specht modules for Iwahori--Hecke algebras of type A when the parameter q equals -1, addressing an open problem in the field.

Contribution

It establishes the reducibility of many Specht modules for Iwahori--Hecke algebras at q=-1, advancing understanding of their module structure.

Findings

Proved reducibility for a broad class of Specht modules at q=-1

Addressed an open problem in the representation theory of Hecke algebras

Enhanced classification of modules in type A Hecke algebras

Abstract

The reducibility of the Specht modules for the Iwahori--Hecke algebras in type $A$ is still open in the case where the defining parameter $q$ equals -1. We prove the reducibility of a large class of Specht modules for these algebras.