Reflections and quotients in Coxeter groups

TL;DR

This paper introduces a formula connecting the left descent set of an element in a Coxeter group with the descent sets of its projections on maximal quotients, advancing understanding of Coxeter group structure.

Contribution

It provides a new formula linking descents in Coxeter groups with projections on quotients, generalizing existing descent-related results.

Findings

Derived a formula relating descents and quotients in Coxeter groups

Established a general framework for descent and quotient relations

Enhanced understanding of Coxeter group projections and structure

Abstract

We present a formula relating the set of left descents of an element of a Coxeter group with the sets of left descents of its projections on maximal quotients indexed by simple right descents. This formula is an instance of a general result involving quotients and descents.