Journal of Mathematics of Kyoto University

On dense orbits in the boundary of a Coxeter system

Tetsuya Hosaka

Abstract

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

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

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281975

Digital Object Identifier
doi:10.1215/kjm/1250281975

Mathematical Reviews number (MathSciNet)
MR2206364

Zentralblatt MATH identifier
1098.57002

Citation

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. https://projecteuclid.org/euclid.kjm/1250281975