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The Classification of crystallographic root systems

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

Abstract

In this chapter we classify crystallographic root systems. In view of the discussion in §9–5, we shall then have also achieved a classification of Weyl groups. As we have already mentioned in the introduction to Part III, the study of Weyl groups and crystallographic root systems uses the results about reflection groups from Chapters 1 through 8. In particular, the classification of Weyl groups and crystallographic root systems will turn out to be refinements of the classification of reflection groups obtained in Chapter 8.

Keywords

Root System Root Length Diagram Commute Weyl Group Dynkin Diagram 
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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