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Journal of Lie Theory 17 (2007), No. 2, 337--355
Copyright Heldermann Verlag 2007

Weyl Groups with Coxeter Presentation and Presentation by Conjugation

Georg W. Hofmann
Dept. of Mathematics and Statistics, Dalhousie University, Halifax NS B3H3J5, Canada

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.

Keywords: Weyl group, Coxeter group, root system, presentation of a group, presentation by conjugation, extended affine Weyl group (EAWeG), extended affine root system (EARS).

MSC: 20F55, 17B65, 17B67, 22E65

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