Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups
Abstract
We investigate the class of root systems R obtained by extending an irreducible root system by a torsion-free group G. In this context there is a Weyl group W and a group U with the presentation by conjugation. We show under additional hypotheses that the kernel of the natural homomorphism from U to W is isomorphic to the kernel of the homomorphism from the abelianization of U to that of W. For this we introduce the concept of a symmetric system, a discrete version of the concept of a symmetric space. Mathematics Subject Classification 2000: 20F55, 17B65, 17B67, 22E65, 22E40. Key Words and Phrases: Weyl group, root system, presentation by conjugation, extended affine Weyl group (EAWeG), extended affine root system (EARS), irreducible root system extended by an abelian group.
Cite
@article{arxiv.0712.0104,
title = {Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups},
author = {Georg W. Hofmann},
journal= {arXiv preprint arXiv:0712.0104},
year = {2007}
}
Comments
38 pages