The even isomorphism theorem for Coxeter groups
Author: M. Mihalik
Journal: Trans. Amer. Math. Soc. 359 (2007), 4297-4324
MSC (2000): Primary 20F55; Secondary 20E34
Published electronically: April 16, 2007
MathSciNet review: 2309186
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Abstract: Coxeter groups have presentations where for all , , and if and only if . A fundamental question in the theory of Coxeter groups is: Given two such ``Coxeter" presentations, do they present the same group? There are two known ways to change a Coxeter presentation, generally referred to as twisting and simplex exchange. We solve the isomorphism question for Coxeter groups with an even Coxeter presentation (one in which is even or when ). More specifically, we give an algorithm that describes a sequence of twists and triangle-edge exchanges that either converts an arbitrary finitely generated Coxeter presentation into a unique even presentation or identifies the group as a non-even Coxeter group. Our technique can be used to produce all Coxeter presentations for a given even Coxeter group.
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Affiliation: Department of Mathematics, Vanderbilt University, 1516 Stevenson Center, Nashville, Tennessee 37240
Received by editor(s): February 18, 2004
Received by editor(s) in revised form: August 6, 2005
Published electronically: April 16, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.