Distribution of accumulation points of roots for type $(n-1,1)$ Coxeter groups

Akihiro Higashitani; Ryosuke Mineyama; Norihiro Nakashima

Distribution of accumulation points of roots for type $(n-1,1)$ Coxeter groups

Group Theory 2017-11-08 v6 Combinatorics Dynamical Systems Metric Geometry

Authors: Akihiro Higashitani , Ryosuke Mineyama , Norihiro Nakashima

Abstract

In this paper, we investigate the set of accumulation points of normalized roots of infinite Coxeter groups for certain class of their action. Concretely, we prove the conjecture proposed in [6, Section 3.2] in the case where the equipped Coxeter matrices are of type $(n-1,1)$ , where $n$ is the rank. Moreover, we obtain that the set of such accumulation points coincides with the closure of the orbit of one point of normalized limit roots. In addition, in order to prove our main results, we also investigate some properties on fixed points of the action.

Keywords

coxeter groups accumulation points normalized roots limit roots orbit closure fixed points type (n-1,1)

Cite

@article{arxiv.1212.6617,
  title  = {Distribution of accumulation points of roots for type $(n-1,1)$ Coxeter groups},
  author = {Akihiro Higashitani and Ryosuke Mineyama and Norihiro Nakashima},
  journal= {arXiv preprint arXiv:1212.6617},
  year   = {2017}
}

Comments

23 pages, Nagoya Math. J. to appear

Distribution of accumulation points of roots for type $(n-1,1)$ Coxeter groups

Abstract

Keywords

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