Stability for Representations of Hecke Algebras of type $A$

TL;DR

This paper introduces the concept of stability for sequences of modules over Hecke algebras of type A and proves that finitely generated consistent sequences exhibit representation stability.

Contribution

It defines a new notion of stability for modules over Hecke algebras and establishes that finitely generated sequences are representation stable.

Findings

Finitely generated consistent sequences over Hecke algebras are representation stable.

Introduction of the stability concept for modules over Hecke algebras.

Proof of stability for a broad class of modules.

Abstract

In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.