Volume 7, issue 2 (2007)

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Matching theorems for systems of a finitely generated Coxeter group

Michael L Mihalik, John G Ratcliffe and Steven T Tschantz

Algebraic & Geometric Topology 7 (2007) 919–956

arXiv: math.GR/0501075

Abstract

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.

Keywords
Coxeter groups
References
Publication
Received: 31 March 2006
Published: 20 June 2007
Authors
Michael L Mihalik
Mathematics Department
Vanderbilt University
Nashville TN 37240
USA
John G Ratcliffe
Mathematics Department
Vanderbilt University
Nashville TN 37240
USA
Steven T Tschantz
Mathematics Department
Vanderbilt University
Nashville TN 37240
USA