发表机构
Bar-Ilan University（巴伊兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究以简单图Γ的线图为Coxeter图的单链Coxeter群的换位作用的点稳定子，证明其为有限指数反射子群并确定其Coxeter图，还建立了两类Coxeter群间的有限指数嵌入关系。
AI 中文摘要
我们研究单链Coxeter群，其Coxeter图是某个简单图Γ的线图ℒΓ；这类群通过换位作用在图的顶点集上，目标是详细刻画该作用的点稳定子。对任意树Σ，我们证明该稳定子是有限指数的反射子群，并确定其Coxeter图，由此发现对任意树Σ，存在Coxeter群W(ℒ^[2]Σ)到W(ℒΣ)的有限指数嵌入，其中包含无穷多稳定子本身为单链的情形。
英文摘要
We study simply-laced Coxeter groups whose Coxeter diagram is the line graph $\mathcal{L}Γ$ 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 $W(\mathcal{L}^{[2]}Σ) \hookrightarrow W(\mathcal{L}Σ)$ for any tree $Σ$, including infinitely many cases where the stabilizer itself is simply-laced.
