Minimality of the boundary of a right-angled Coxeter system
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Abstract:
In this paper, we show that the boundary $\partial \Sigma (W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{\tilde {S}}$ is irreducible, where $W_{\tilde {S}}$ is the minimum parabolic subgroup of finite index in $W$. We also provide several applications and remarks. In particular, we show that for a right-angled Coxeter system $(W,S)$, the set $\{w^{\infty } | w\in W, o(w)=\infty \}$ is dense in the boundary $\partial \Sigma (W,S)$.References
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Additional Information
- Tetsuya Hosaka
- Affiliation: Department of Mathematics, Faculty of Education, Utsunomiya University, Utsuno-miya, 321-8505, Japan
- Email: hosaka@cc.utsunomiya-u.ac.jp
- Received by editor(s): November 20, 2006
- Received by editor(s) in revised form: March 25, 2008
- Published electronically: September 24, 2008
- Additional Notes: The author was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 18740025).
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 899-910
- MSC (2000): Primary 20F65, 20F55
- DOI: https://doi.org/10.1090/S0002-9939-08-09585-3
- MathSciNet review: 2457429