Reducing Rouquier Complexes

TL;DR

This paper introduces a method to obtain simplified representatives for positive Rouquier complexes using Morse theoretical Gaussian elimination, resulting in a more efficient understanding of their structure.

Contribution

The paper presents a novel reduction technique for Rouquier complexes that preserves their graded structure while simplifying their representation.

Findings

Reduced representatives are obtained via Morse theoretical Gaussian elimination.

The underlying graded object remains a direct sum of Bott-Samelson objects.

The approach simplifies the analysis of Rouquier complexes.

Abstract

We describe reduced representatives for positive Rouquier complexes. These are obtained via Morse theoretical Gaussian elimination from the corresponding standard representatives. The underlying graded object is still a direct sum of Bott-Samelson objects, but over subwords rather than subexpressions.