Reflections and quotients in Coxeter groups

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.

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Publication Details

Journal
Comptes Rendus Mathématique
Published
2025-04-08
DOI
https://doi.org/10.5802/crmath.714
Primary Topic
Advanced Combinatorial Mathematics
Type
article
Field-Weighted Citation Impact
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article

Reflections and quotients in Coxeter groups

Paolo Sentinelli
Comptes Rendus Mathématique
Advanced Combinatorial Mathematics
article

Reflections and quotients in Coxeter groups

Paolo Sentinelli
article en

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.

Comptes Rendus MathématiqueVol. 363(G3)
Openalex Percentile: Top 89%
Advanced Combinatorial Mathematics
DOIOpen Access PDFOpenAlex
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Reflections and quotients in Coxeter groups — Paolo Sentinelli · Comptes Rendus Mathématique (2025) | TGRS Research Map | TGRS