Demazure product and hopping in type D

TL;DR

This paper extends the combinatorial description of the Demazure product, also known as the 0-Hecke product, from permutations to type D Coxeter groups, enhancing understanding of its properties and applications.

Contribution

It provides a new combinatorial characterization of the Demazure product specifically for type D Coxeter groups, building on previous work for permutations.

Findings

Extended the combinatorial description of Demazure product to type D Coxeter groups

Provided new insights into the properties of the Demazure product in type D

Enhanced the toolkit for working with Coxeter groups and their applications

Abstract

The Demazure product, also called the 0-Hecke product, is an associative operation on Coxeter groups with interesting properties and applications. In (Li et al 2024) it was shown that the Demazure product of two permutations can be described purely combinatorially: using only their one-line notation and not relying on reduced words. In this paper, we extend this to type D Coxeter groups.