Dense subsets of the boundary of a Coxeter system

Tetsuya Hosaka
2004 Proceedings of the American Mathematical Society  
In this paper, we investigate dense subsets of the boundary of a Coxeter system. We show that for a Coxeter system (W, S), if W {s 0 } is quasi-dense in W and the order o(s 0 t 0 ) = ∞ for some s 0 , t 0 ∈ S, then there exists a point α in the boundary ∂Σ(W, S) of the Coxeter system (W, S) such that the orbit W α is dense in ∂Σ(W, S). Here
doi:10.1090/s0002-9939-04-07480-5 fatcat:rcxel6x4l5euzouxrmjgqykhn4