Advertisement

Fundamental systems

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

Abstract

In this chapter we introduce fundamental systems for root systems. Just as a root system is a translation into linear algebra of the reflecting hyperplanes of a finite reflection group, so a fundamental system is a linear algebra version of a Weyl chamber of the group. The discussion of fundamental systems in this chapter largely amounts to the construction of a one-to-one correspondence between chambers and fundamental systems. We shall also introduce, in the final section of this chapter, the important concept of height.

Keywords

Root System Nonzero Entry Fundamental System Root Vector Weyl Chamber 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations