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arXiv · 0712.0104

Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups

Georg W. Hofmann
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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.

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Georg W. Hofmann. 2007-12-05. Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups. https://arxiv.org/abs/0712.0104

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