Abstract
Coxeter elements form a distinguished conjugacy class in each finite Euclidean reflection group. This chapter concerns their order. We shall show that, for an irreducible reflection group, the order of a Coxeter element can be expressed in terms of the associated root system. Coxeter elements will be treated again in Chapters 32 and 34 when we discuss regular elements. In this chapter, as a preliminary result, we shall prove that Coxeter elements are regular. The results of this chapter are independent of those in Chapters 27 and 28.
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© 2001 Springer Science+Business Media New York
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Kane, R., Borwein, J., Borwein, P. (2001). Coxeter elements. 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_30
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DOI: https://doi.org/10.1007/978-1-4757-3542-0_30
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3194-8
Online ISBN: 978-1-4757-3542-0
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