Classifications of pseudo-reflection groups

  • Richard Kane
  • Jonathan Borwein
  • Peter Borwein
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

In this chapter, we sketch some of the classification results obtained for pseudo-reflection groups in the nonmodular case. The classification results given in this chapter are not used elsewhere, and are simply given as illustrations of the type of patterns that hold. We begin by sketching the Shephard-Todd classification of the finite complex pseudo-reflection groups. We then explain how this classification can be used to obtain classifications of pseudo-reflection groups over other fields. The Shephard-Todd classification is the key to all other classifications described in this chapter. We shall omit most details, and only sketch arguments.

Keywords

Classification Result Invariant Theory Valuation Ring Infinite Family Reflection Group 
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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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Richard Kane
    • 1
  • Jonathan Borwein
    • 2
  • Peter Borwein
    • 2
  1. 1.Department of MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada

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