A Class of Reflection Rigid Coxeter Systems
نویسنده
چکیده
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.
منابع مشابه
A Class of Rigid Coxeter Groups
A Coxeter group W is said to be rigid if, given any two Coxeter systems (W,S) and (W,S′), there is an automorphism ρ : W −→ W such that ρ(S) = S′. We consider the class of Coxeter systems (W,S) for which the Coxeter graph ΓS is complete and has only odd edge labels (such a system is said to be of “type Kn”). It is shown that if W has a type Kn system, then any other system for W is also type Kn...
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تاریخ انتشار 2005