Positivity and Web Bases for Specht Modules of Hecke Algebras

TL;DR

This paper proves that for certain Specht modules of Hecke algebras, the change of basis matrix from the standard to web basis is unitriangular and positive, extending previous results to modules with at most two-part partitions.

Contribution

It establishes the positivity and unitriangularity of the transition matrix for Specht modules labeled by partitions with at most two parts, generalizing prior work.

Findings

Transition matrix is unitriangular.

Matrix satisfies strong positivity.

Results apply to modules with at most two parts.

Abstract

We show that the transition matrix from the standard basis to the web basis for a Specht module of the Hecke algebra is unitriangular and satisfies a strong positivity property whenever the Specht module is labeled by a partition with at most two parts. This generalizes results of Russell--Tymoczko and Rhoades.