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Locally finite root systems

About this Title

Ottmar Loos and Erhard Neher

Publication: Memoirs of the American Mathematical Society
Publication Year: 2004; Volume 171, Number 811
ISBNs: 978-0-8218-3546-3 (print); 978-1-4704-0412-3 (online)
DOI: https://doi.org/10.1090/memo/0811
MathSciNet review: 2073220
MSC: Primary 17B20; Secondary 17B65, 17B70

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Table of Contents

Chapters

  • Introduction
  • 1. The category of sets in vector spaces
  • 2. Finiteness conditions and bases
  • 3. Locally finite root systems
  • 4. Invariant inner products and the coroot system
  • 5. Weyl groups
  • 6. Integral bases, root bases and Dynkin diagrams
  • 7. Weights and coweights
  • 8. Classification
  • 9. More on Weyl groups and automorphism groups
  • 10. Parabolic subsets and positive systems for symmetric sets in vector spaces
  • 11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group
  • 12. Closed and full subsystems of finite and infinite classical root systems
  • 13. Parabolic subsets of root systems: classification
  • 14. Positive systems in root systems
  • 15. Positive linear forms and facets
  • 16. Dominant and fundamental weights
  • 17. Gradings of root systems
  • 18. Elementary relations and graphs in 3-graded root systems