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Coxeter complexes

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Part of the Lecture Notes in Mathematics book series (LNM,volume 386)

Abstract

A complex Σ is called a Coxeter complex if it is a thin chamber complex, and if for every pair (C, C′) of adjacent chambers, there exists a root containing C and not C′, which means, in other words, that there exists a folding of Σ which maps C′ onto C. In this section 2, the letter Σ will always denote a Coxeter complex. The group generated by all reflections of a Coxeter complex Σ will be denoted by W(Σ) and called the Weyl group of Σ.

Keywords

  • Convex Hull
  • Weyl Group
  • Finite Type
  • Coxeter Group
  • Coxeter System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1974 Springer-Verlag Berlin Heidelberg

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(1974). Coxeter complexes. In: Buildings of Spherical Type and Finite BN-Pairs. Lecture Notes in Mathematics, vol 386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38349-9_2

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  • DOI: https://doi.org/10.1007/978-3-540-38349-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06757-3

  • Online ISBN: 978-3-540-38349-9

  • eBook Packages: Springer Book Archive