ENGLISH

Introduction to Complex Reflection Groups and Their Braid Groups

By Michel Broué (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2010
ISBN
3642111742, 9783642111747
DOI
10.1007/978-3-642-11175-4
Language
english
Format
PDF
Filesize
1 MB (1254395 bytes)
Series
Lecture Notes in Mathematics 1988
Edition
1
Pages
144\155
Scanned
yes
Time added
2011-06-04 13:46:07
Group Theory and Generalizations; Commutative Ring

Description

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.

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