Abstract
In this chapter we classify crystallographic root systems. In view of the discussion in §9–5, we shall then have also achieved a classification of Weyl groups. As we have already mentioned in the introduction to Part III, the study of Weyl groups and crystallographic root systems uses the results about reflection groups from Chapters 1 through 8. In particular, the classification of Weyl groups and crystallographic root systems will turn out to be refinements of the classification of reflection groups obtained in Chapter 8.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kane, R., Borwein, J., Borwein, P. (2001). The Classification of crystallographic root systems. In: Borwein, J., Borwein, P. (eds) Reflection Groups and Invariant Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3542-0_11
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3542-0_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3194-8
Online ISBN: 978-1-4757-3542-0
eBook Packages: Springer Book Archive