Abstract
We can pass from the Weyl group of a crystallographic root system and form an infinite group that has more information about the root system, and yet still possesses a structure analogous to that of the Weyl group. Notably, it has a Coxeter group structure. This group is called the affine Weyl group. Affine Weyl groups have a number of uses. They will be used in Chapter 12 to analyze subroot systems of crystallographic root systems. They are even useful for understanding ordinary Weyl groups. This will be demonstrated in §11–6.
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© 2001 Springer Science+Business Media New York
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Kane, R., Borwein, J., Borwein, P. (2001). Affine Weyl groups. 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_12
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DOI: https://doi.org/10.1007/978-1-4757-3542-0_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3194-8
Online ISBN: 978-1-4757-3542-0
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