2005/02/13 by Tetsuya Hosaka, Hosaka, Tetsuya
Mathematics · #20F55 #20F65 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #msc:20F55 #msc:20F65
paper · pdf · doi:10.48550/arxiv.math/0502271
Part 3 of 3
arxiv created 2005/02/13 · openalex publication_date 2005/02/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give a new class of rigid Coxeter groups. Let (W,S) be a Coxeter system. Suppose that (0) for each s,t∈ S such that m(s,t) is even, m(s,t)∈\2\∪ 4\N, (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 group W is rigid. This is an extension of a result of D.Radcliffe.