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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimality of the boundary of a right-angled Coxeter system


Author: Tetsuya Hosaka
Journal: Proc. Amer. Math. Soc. 137 (2009), 899-910
MSC (2000): Primary 20F65, 20F55
Published electronically: September 24, 2008
MathSciNet review: 2457429
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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}\,\vert\,w\in W, o(w)=\infty\}$ is dense in the boundary $ \partial\Sigma(W,S)$.


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

DOI: http://dx.doi.org/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
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.