Proceedings of the American Mathematical Society

Author(s): Tetsuya Hosaka
Journal: Proc. Amer. Math. Soc. 137 (2009), 899-910.
MSC (2000): Primary 20F65, 20F55
Posted: September 24, 2008
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Abstract: In this paper, we show that the boundary $\partial\Sigma(W,S)$ of a right-angled Coxeter system

is minimal if and only if $W_{\tilde{S}}$ is irreducible, where $W_{\tilde{S}}$ is the minimum parabolic subgroup of finite index in

. We also provide several applications and remarks. In particular, we show that for a right-angled Coxeter system

, the set $\{w^{\infty}\,\vert\,w\in W, o(w)=\infty\}$ is dense in the boundary $\partial\Sigma(W,S)$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20F65, 20F55

Tetsuya Hosaka
Affiliation: Department of Mathematics, Faculty of Education, Utsunomiya University, Utsunomiya, 321-8505, Japan
Email: hosaka@cc.utsunomiya-u.ac.jp

DOI: 10.1090/S0002-9939-08-09585-3
PII: S 0002-9939(08)09585-3
Keywords: Boundaries of Coxeter groups
Received by editor(s): November 20, 2006,
Received by editor(s) in revised form: March 25, 2008
Posted: 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 of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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