Abstract
The goal of this chapter is to introduce Euclidean reflection groups. This will be done in two ways. First of all, examples of reflection groups, in the plane and in 3-space, are discussed in detail. Secondly, we provide, via a preliminary discussion of Weyl chambers and invariant theory, a suggestion of the beautiful structure theorems that hold for reflection groups, and that explain the interest in such groups. The dihedral and symmetric groups will receive particular attention.
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© 2001 Springer Science+Business Media New York
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Kane, R., Borwein, J., Borwein, P. (2001). Euclidean reflection 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_2
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DOI: https://doi.org/10.1007/978-1-4757-3542-0_2
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