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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Additional Information

**M. Mihalik**

Affiliation:
Department of Mathematics, Vanderbilt University, 1516 Stevenson Center, Nashville, Tennessee 37240

DOI:
http://dx.doi.org/10.1090/S0002-9947-07-04133-5

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.