Minimality of the boundary of a right-angled Coxeter system

Hosaka, Tetsuya

doi:10.1090/S0002-9939-08-09585-3

Minimality of the boundary of a right-angled Coxeter system
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Proc. Amer. Math. Soc. 137 (2009), 899-910 Request permission

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 $\partial \Sigma (W,S)$.

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