Reflection factorizations and quasi-Coxeter elements

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Original languageEnglish
Pages (from-to)127-157
Number of pages31
JournalJournal of Combinatorial Algebra
Volume7
Issue number1
Publication statusPublished - 25 May 2023

Abstract

We investigate the so-called dual Matsumoto property or Hurwitz action in finite, affine and arbitrary Coxeter groups. In particular, we want to investigate how to reduce reflection factorizations and how two reflection factorizations of the same element are related to each other. We are motivated by the dual approach to Coxeter groups proposed by Bessis and the question whether there is an anlogue of the well known Matsumoto property for reflection factorizations. Our aim is a substantial understanding of the Hurwitz action. We therefore reprove uniformly results of Lewis and Reiner as well as Baumeister, Gobet, Roberts and the first author on the Hurwitz in finite Coxeter groups. Further we show that in an arbitrary Coxeter group all reduced reflection factorizations of the same element appear in the same Hurwitz orbit after a suitable extension by simple reflections. As parabolic quasi-Coxeter elements play an outstanding role in the study of the Hurwitz action, we aim to characterize these elements. We give characterizations of maximal parabolic quasi-Coxeter elements in arbitrary Coxeter groups as well as a characterization of all parabolic quasi-Coxeter elements in affine Coxeter groups.

Keywords

    absolute order, Coxeter groups, Hurwitz action, quasi-Coxeter elements, reflection factorizations

ASJC Scopus subject areas

Cite this

Reflection factorizations and quasi-Coxeter elements. / Wegener, Patrick; Yahiatene, Sophiane.
In: Journal of Combinatorial Algebra, Vol. 7, No. 1, 25.05.2023, p. 127-157.

Research output: Contribution to journalArticleResearchpeer review

Wegener, P & Yahiatene, S 2023, 'Reflection factorizations and quasi-Coxeter elements', Journal of Combinatorial Algebra, vol. 7, no. 1, pp. 127-157. https://doi.org/10.4171/JCA/70
Wegener, P., & Yahiatene, S. (2023). Reflection factorizations and quasi-Coxeter elements. Journal of Combinatorial Algebra, 7(1), 127-157. https://doi.org/10.4171/JCA/70
Wegener P, Yahiatene S. Reflection factorizations and quasi-Coxeter elements. Journal of Combinatorial Algebra. 2023 May 25;7(1):127-157. doi: 10.4171/JCA/70
Wegener, Patrick ; Yahiatene, Sophiane. / Reflection factorizations and quasi-Coxeter elements. In: Journal of Combinatorial Algebra. 2023 ; Vol. 7, No. 1. pp. 127-157.
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