2005/02/13 by Tetsuya Hosaka, Hosaka, Tetsuya
Mathematics · #20F55 #20F65 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F55 #msc:20F65
paper · pdf · doi:10.48550/arxiv.math/0502269
Part 1 of 3
arxiv created 2005/02/13 · arxiv updated 2009/12/01
In this paper, we give a class of reflection rigid Coxeter systems. Let (W,S) be a Coxeter system. Suppose that (1) for each s,t∈ S such that m(s,t) is odd, \s,t\ is a maximal spherical subset of S, (2) there does not exist a three-points subset \s,t,u\⊂ S such that m(s,t) and m(t,u) are odd, and (3) for each s,t∈ S such that m(s,t) is odd, the number of maximal spherical subsets of S intersecting with \s,t\ is at most two, where m(s,t) is the order of st in the Coxeter group W. Then we show that the Coxeter system (W,S) is reflection rigid. This is an extension of a result of N.Brady, J.P.McCammond, B.Mühlherr and W.D.Neumann.