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Symmetric presentations of Coxeter groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  20 June 2011

Ben Fairbairn
Ben Fairbairn
Affiliation:
Departamento de Matemáticas, Universidad de Los Andes, Carrera 1 No. 18A-12, Bogotá, Colombia
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Abstract

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We apply the techniques of symmetric generation to establish the standard presentations of the finite simply laced irreducible finite Coxeter groups, that is, the Coxeter groups of types An, Dn and En, and show that these are naturally arrived at purely through consideration of certain natural actions of symmetric groups. We go on to use these techniques to provide explicit representations of these groups.

Keywords

symmetric generationCoxeter group

MSC classification

Secondary: 20F55: Reflection and Coxeter groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 669 - 683
Copyright
Copyright © Edinburgh Mathematical Society 2011

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