A New Proof for Classification of Irreducible Modules of a Hecke Algebra of Type $ A_n$

TL;DR

This paper presents a novel proof for classifying irreducible modules of affine Hecke algebras of type A_n, providing an alternative approach to Murphy's 1995 classification.

Contribution

It introduces a new proof method for the classification of irreducible modules, enhancing understanding of affine Hecke algebra representations.

Findings

New proof technique for module classification

Simplifies understanding of affine Hecke algebra representations

Provides an alternative to Murphy's original proof

Abstract

In this paper we give a new proof for the classification of irreducible modules of an affine Hecke algebra of type $A_n$, which was obtained by G. E. Murphy in 1995.