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

Akihiro Higashitani; Ryosuke Mineyama; Norihiro Nakashima

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arXiv · 1212.6617

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

Akihiro Higashitani·Ryosuke Mineyama·Norihiro Nakashima

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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.

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BibTeX RIS

Akihiro Higashitani, Ryosuke Mineyama, Norihiro Nakashima. 2012-12-29. Distribution of accumulation points of roots for type $(n-1,1)$ Coxeter groups. https://arxiv.org/abs/1212.6617

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