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ISSN 1088-6826(e) ISSN 0002-9939(p)

Minimality of the boundary of a right-angled Coxeter system

Author(s): Tetsuya Hosaka
Journal: Proc. Amer. Math. Soc. 137 (2009), 899-910.
MSC (2000): Primary 20F65, 20F55
Posted: 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 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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