Weyl Groups with Coxeter Presentation and Presentation by Conjugation

Abstract

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.

23 pages

Cited by in corpus (5)

• Groups of extended affine Lie type
• The Weyl group of type $A_1$ root systems extended by an abelian group
• Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups
• A Length Function for Weyl Groups of extended affine root systems of Type $A_1$
• Extended affine Weyl groups: Presentation by conjugation via integral collection