A simple characterization of special matchings in lower Bruhat intervals

TL;DR

This paper provides a straightforward way to characterize special matchings within lower Bruhat intervals of Coxeter groups, enhancing understanding of their structure and actions.

Contribution

It introduces a simple characterization of special matchings in lower Bruhat intervals, offering new insights into their properties and actions.

Findings

Simplified characterization of special matchings

Results on the action of special matchings

Enhanced understanding of Bruhat interval structure

Abstract

We give a simple characterization of special matchings in lower Bruhat intervals (that is, intervals starting from the identity element) of a Coxeter group. As a byproduct, we obtain some results on the action of special matchings.