Skip to content
DraconiticResearch
Search Sources API
190,851 studies31 sourcesUpdated 47 min ago
PreprintarXiv licencearXiv

Prefixes of Coxeter elements are Coxeter elements of the reflection subgroups they generate

  • Patrick Wegener
Open at sourcePDFDOICite

Abstract

Let (W,S) be a Coxeter system of finite rank, let T be its set of reflections and let c ∈ W be a Coxeter element. For x in the interval [1,c]T of the absolute order, let P(x) be the subgroup generated by the reflections t≤T x. We prove that x is a Coxeter element of P(x) with respect to the canonical Coxeter generators of P(x), that P(x) is generated by the factors of any reduced reflection factorization of x, and that the Hurwitz action on the reduced reflection factorizations of x is transitive. The proof reduces the general case to the case of a Coxeter system whose Coxeter matrix has entries in {1,2,3,∞}, which was treated by Hubery and Krause.

Related

  1. Maximal ranks of free abelian subgroups of generalized cactus groups associated with finite Coxeter systems
    Jan Kim, Junseok Kim
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  2. Noncrossing combinatorics of quasi-Coxeter elements
    Eugenio Cainelli, Giovanni Paolini, Riccardo Zaccaria
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. The restricted Hurwitz action on cameral decompositions of Coxeter elements
    Emir Melliti
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. A lower bound on the density of prefixes with maximal palindromic length
    Josef Rukavicka
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Conformal Certification of Reasoning Trace Prefixes
    Matt Y. Cheung, Ashok Veeraraghavan, Hanjie Chen +1
    arXivPreprintCC BY 4.0Full textStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{wegener2026prefixes,
  title = {{Prefixes of Coxeter elements are Coxeter elements of the reflection subgroups they generate}},
  author = {Patrick Wegener},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19755},
  eprint = {2610.19755},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19755},
}
RIS
TY  - UNPB
TI  - Prefixes of Coxeter elements are Coxeter elements of the reflection subgroups they generate
AU  - Patrick Wegener
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19755
UR  - https://arxiv.org/abs/2610.19755
AB  - Let (W,S) be a Coxeter system of finite rank, let T be its set of reflections and let c ∈ W be a Coxeter element. For x in the interval [1,c]_T of the absolute order, let P(x) be the subgroup generated by the reflections t≤_T x. We prove that x is a Coxeter element of P(x) with respect to the canonical Coxeter generators of P(x), that P(x) is generated by the factors of any reduced reflection factorization of x, and that the Hurwitz action on the reduced reflection factorizations of x is transitive. The proof reduces the general case to the case of a Coxeter system whose Coxeter matrix has entries in {1,2,3,∞}, which was treated by Hubery and Krause.
ER  -