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- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1988)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
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)Authors and Affiliations
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Inst. Mathématiques Jussieu, Université Paris VII, Paris, France
Michel Broué
Bibliographic Information
Book Title: Introduction to Complex Reflection Groups and Their Braid Groups
Authors: Michel Broué
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-11175-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Softcover ISBN: 978-3-642-11174-7Published: 17 February 2010
eBook ISBN: 978-3-642-11175-4Published: 28 January 2010
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 144
Topics: Group Theory and Generalizations, Commutative Rings and Algebras, Associative Rings and Algebras, Algebraic Topology