On Dense Orbits in the Boundary of a Coxeter System
نویسنده
چکیده
In this paper, we study the minimality of the boundary of a Coxeter system. We show that for a Coxeter system (W,S) if there exist a maximal spherical subset T of S and an element s0 ∈ S such that m(s0, t) ≥ 3 for each t ∈ T and m(s0, t0) = ∞ for some t0 ∈ T , then every orbit Wα is dense in the boundary ∂Σ(W,S) of the Coxeter system (W,S), hence ∂Σ(W,S) is minimal, where m(s0, t) is the order of s0t in W .
منابع مشابه
On Boundaries of Parabolic Subgroups of Coxeter Groups
In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let (W, S) be a Coxeter system and let T be a subset of S such that the parabolic subgroup WT is infinite. Then we show that if a certain set is quasi-dense in W , then W∂Σ(WT , T ) is dense in the boundary ∂Σ(W, S) of the Coxeter system (W, S), where ∂Σ(WT , T ) is the boundary of (WT , T ).
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