Details
| Original language | English |
|---|---|
| Pages (from-to) | 127-157 |
| Number of pages | 31 |
| Journal | Journal of Combinatorial Algebra |
| Volume | 7 |
| Issue number | 1 |
| Publication status | Published - 25 May 2023 |
Abstract
Keywords
- absolute order, Coxeter groups, Hurwitz action, quasi-Coxeter elements, reflection factorizations
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of Combinatorial Algebra, Vol. 7, No. 1, 25.05.2023, p. 127-157.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Reflection factorizations and quasi-Coxeter elements
AU - Wegener, Patrick
AU - Yahiatene, Sophiane
N1 - Publisher Copyright: © 2023 European Mathematical Society Published by EMS Press.
PY - 2023/5/25
Y1 - 2023/5/25
N2 - 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.
AB - 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.
KW - absolute order
KW - Coxeter groups
KW - Hurwitz action
KW - quasi-Coxeter elements
KW - reflection factorizations
UR - http://www.scopus.com/inward/record.url?scp=85168638317&partnerID=8YFLogxK
U2 - 10.4171/JCA/70
DO - 10.4171/JCA/70
M3 - Article
VL - 7
SP - 127
EP - 157
JO - Journal of Combinatorial Algebra
JF - Journal of Combinatorial Algebra
SN - 2415-6302
IS - 1
ER -