A cell filtration of the restriction of a cell module

TL;DR

This paper provides a new proof demonstrating that restricting a cell module of the Hecke algebra of the symmetric group maintains a filtration by cell modules, enhancing understanding of module structure.

Contribution

The paper introduces a novel proof technique for the filtration property of restricted cell modules in Hecke algebras, offering new insights into their structure.

Findings

Restriction of a cell module has a filtration by cell modules

New proof technique established for module filtration

Clarifies structure of Hecke algebra modules

Abstract

We give a new proof that the restriction of a cell module of the Hecke algebra of the symmetric group on $n$ letters, to the Hecke algebra of the symmetric group on $n-1$ letters, has a filtration by cell modules.