Weyl groups associated with affine reflection systems of type A1 (Coxeter type dening relations)

Abstract

We offer a presentation for the Weyl group of an affine reection system R of type A1 as well as a presentation for the so called hyperbolic Weyl group associated with an affine reection system of type A1. Applying these presentations to extended affine Weyl groups, and using a description of the center of the hyperbolic Weyl group, we also give a new finite presentation for an extended affine Weyl group of type A1. Our presentation for the (hyperbolic) Weyl group of an affine reection system of type A1 is the first nontrivial presentation given in this generality, and can be considered as a model for other types. © 2013 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.