On boundaries of parabolic subgroups of Coxeter groups

2005/02/13 by Tetsuya Hosaka, Hosaka, Tetsuya
Mathematics · #20F55 #20F65 #57M07 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F55 #msc:20F65 #msc:57M07

paper · pdf · doi:10.48550/arxiv.math/0502268

the full version of the paper "Addendum to `Dense subsets of the boundary of a Coxeter system'"

arxiv created 2005/02/13 · arxiv updated 2009/12/01

Abstract

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 W_T is infinite. Then we show that if a certain set is quasi-dense in W, then W ∂Σ(W_T,T) is dense in the boundary ∂Σ(W,S) of the Coxeter system (W,S), where ∂Σ(W_T,T) is the boundary of (W_T,T).

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• A Note on Parabolic Subgroups of a Coxeter Group
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