PreprintCC BY 4.0arXiv
Stabilizers in Coxeter groups with a transpositional action
Abstract
We study simply-laced Coxeter groups whose Coxeter diagram is the line graph ℒΓ of some simple graph Γ; such groups act on the set of vertices of the graph by transpositions. Our goal is to describe the point stabilizer of this action in detail. For any tree Σ, we show that the stabilizer is a finite-index reflection subgroup, and identify its Coxeter diagram, thereby discovering finite-index embeddings of Coxeter groups W(ℒ[2]Σ) ↪ W(ℒΣ) for any tree Σ, including infinitely many cases where the stabilizer itself is simply-laced.
Related
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BibTeX
@misc{cohen2026stabilizers,
title = {{Stabilizers in Coxeter groups with a transpositional action}},
author = {Noa Cohen and Uzi Vishne},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01309},
eprint = {2609.01309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01309},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stabilizers in Coxeter groups with a transpositional action
AU - Noa Cohen
AU - Uzi Vishne
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01309
UR - https://arxiv.org/abs/2609.01309
AB - We study simply-laced Coxeter groups whose Coxeter diagram is the line graph ℒΓ of some simple graph Γ; such groups act on the set of vertices of the graph by transpositions. Our goal is to describe the point stabilizer of this action in detail. For any tree Σ, we show that the stabilizer is a finite-index reflection subgroup, and identify its Coxeter diagram, thereby discovering finite-index embeddings of Coxeter groups W(ℒ^[2]Σ) ↪ W(ℒΣ) for any tree Σ, including infinitely many cases where the stabilizer itself is simply-laced.
ER -