Lecture Notes in Mathematics

Introduction to Complex Reflection Groups and Their Braid Groups

Authors: Broué, Michel

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About this book

Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra.

It has recently been discovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductive groups. It is now also broadly agreed upon that many of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic properties of complex reflection groups (characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basic definitions and properties of the associated braid groups, as well as a quick introduction to Bessis' lifting of Springer theory to braid groups.

Reviews

From the reviews:

“It is the aim of the present notes to give an introduction to complex reflection groups in such a way as to lead the reader to the very forefront of research in this area. … it is a useful addition to the growing literature on complex reflection groups.” (Stephen P. Humphries, Mathematical Reviews, Issue 2011 d)

Table of contents (1 chapters)

  • Prerequisites and Complements in Commutative Algebra

    Michel Broué

    Pages 11-33

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-11175-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-11174-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Complex Reflection Groups and Their Braid Groups
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1988
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-11175-4
DOI
10.1007/978-3-642-11175-4
Softcover ISBN
978-3-642-11174-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 144
Topics