Graded Specht modules

TL;DR

This paper introduces a grading on Specht modules over cyclotomic Hecke algebras, extending recent work on graded structures in symmetric group algebras to these more general algebraic objects.

Contribution

It provides a method to grade Specht modules over cyclotomic Hecke algebras, building on recent developments in graded algebra structures.

Findings

Established a grading on Specht modules over cyclotomic Hecke algebras

Extended the grading framework from symmetric groups to more general algebras

Facilitated new algebraic and representation-theoretic insights

Abstract

Recently, the first two authors have defined a Z-grading on group algebras of symmetric groups and more generally on the cyclotomic Hecke algebras of type G(l,1,d). In this paper we explain how to grade Specht modules over these algebras.