Symmetric Presentations of Coxeter Groups

Details Symmetric Presentations of Coxeter Groups Symmetric Presentations of Coxeter Groups

2011-04-29

arxiv.org/abs/1104.5595v1

Mathematics

Group Theory

This is the predecessor of arXiv:0901.2660v1. To appear in the Proceedings of the Edinburgh Mathematical Society

Scientific paper

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.

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