Dense subsets of the boundary of a Coxeter system
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- by Tetsuya Hosaka PDF
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Addendum: Proc. Amer. Math. Soc. 133 (2005), 3745-3747.
Abstract:
In this paper, we investigate dense subsets of the boundary of a Coxeter system. We show that for a Coxeter system $(W,S)$, if $W^{\{s_0\}}$ is quasi-dense in $W$ and the order $o(s_0t_0)=\infty$ for some $s_0,t_0\in S$, then there exists a point $\alpha$ in the boundary $\partial \Sigma (W,S)$ of the Coxeter system $(W,S)$ such that the orbit $W\alpha$ is dense in $\partial \Sigma (W,S)$. Here $W^{\{s_0\}}=\{w\in W | \ell (ws)<\ell (w) \ \text {for each}\ s\in S\setminus \{s_0\} \}\setminus \{1\}$. We also show that if the set $\bigcup \{W^{\{s\}} | s\in S \ \text {such that}\ o(st)=\infty \ \text {for some}\ t\in S\}$ is quasi-dense in $W$, then $\{w^\infty | w\in W \ \text {such that}\ o(w)=\infty \}$ is dense in $\partial \Sigma (W,S)$.References
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Additional Information
- Tetsuya Hosaka
- Affiliation: Department of Mathematics, Utsunomiya University, Utsunomiya, 321-8505, Japan
- Email: hosaka@cc.utsunomiya-u.ac.jp
- Received by editor(s): April 15, 2003
- Received by editor(s) in revised form: August 4, 2003
- Published electronically: May 12, 2004
- Additional Notes: The author was partly supported by a Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan, (No. 15740029)
- Communicated by: Ronald A. Fintushel
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3441-3448
- MSC (2000): Primary 57M07, 20F65, 20F55
- DOI: https://doi.org/10.1090/S0002-9939-04-07480-5
- MathSciNet review: 2073322