Geodesic
Matching theorems for systems of a finitely generated Coxeter group
Mihalik, Michael1 ; Ratcliffe, John G1 ; Tschantz, Steven T1
1Mathematics Department, Vanderbilt University, Nashville TN 37240, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 919-956
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We study the relationship between two sets S and S′ of Coxeter generators of a finitely generated Coxeter group W by proving a series of theorems that identify common features of S and S′. We describe an algorithm for constructing from any set of Coxeter generators S of W a set of Coxeter generators R of maximum rank for W.

A subset C of S is called complete if any two elements of C generate a finite group. We prove that if S and S′ have maximum rank, then there is a bijection between the complete subsets of S and the complete subsets of S′ so that corresponding subsets generate isomorphic Coxeter systems. In particular, the Coxeter matrices of (W,S) and (W,S′) have the same multiset of entries.

DOI : 10.2140/agt.2007.7.919
Keywords: Coxeter groups

Mihalik, Michael  1   ; Ratcliffe, John G  1   ; Tschantz, Steven T  1

1 Mathematics Department, Vanderbilt University, Nashville TN 37240, USA 
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Mihalik, Michael; Ratcliffe, John G; Tschantz, Steven T. Matching theorems for systems of a finitely generated Coxeter group. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 919-956. doi: 10.2140/agt.2007.7.919

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