Journal of Mathematics of Kyoto University

On dense orbits in the boundary of a Coxeter system

Tetsuya Hosaka

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In this paper, we study the minimality of the boundary of a Coxeter system. We show that for a Coxeter system $(W, S)$ if there exist a maximal spherical subset $T$ of $S$ and an element $s_{0} \in S$ such that $m(s_{0}, t) \geq 3$ for each $t \in T$ and $m(s_{0}, t_{0}) = \infty$ for some $t_{0} \in T$, then every orbit $W\alpha$ is dense in the boundary $\partial \Sigma (W, S)$ of the Coxeter system $(W, S)$, hence $\partial \Sigma (W, S)$ is minimal, where $m(s_{0}, t)$ is the order of $s_{0}t$ in $W$.

Article information

J. Math. Kyoto Univ., Volume 45, Number 3 (2005), 627-631.

First available in Project Euclid: 14 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M07: Topological methods in group theory
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]


Hosaka, Tetsuya. On dense orbits in the boundary of a Coxeter system. J. Math. Kyoto Univ. 45 (2005), no. 3, 627--631. doi:10.1215/kjm/1250281975.

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