Weyl Groups with Coxeter Presentation and Presentation by Conjugation

Details Weyl Groups with Coxeter Presentation and Presentation by Conjugation Weyl Groups with Coxeter Presentation and Presentation by Conjugation

2006-07-22

arxiv.org/abs/math/0607562v1

Journal of Lie Theory, 17 (2007)

Mathematics

Group Theory

23 pages

Scientific paper

We investigate which Weyl groups have a Coxeter presentation and which of them at least have the presentation by conjugation with respect to their root system. For most concepts of root systems the Weyl group has both. In the context of extended affine root systems (EARS) there is a small subclass allowing a Coxeter presentation of the Weyl group and a larger subclass allowing the presentation by conjugation. We give necessary and sufficient conditions for both classes. Our results entail that every extended affine Weyl group (EAWeG) has the presentation by conjugation with respect to a suitable EARS.

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