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Introduction to Complex Reflection Groups and Their Braid Groups / by Michel Broué

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink Bücher | Lecture notes in mathematics ; 1988Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Description: Online-Ressource (XI, 138p, digital)ISBN:
  • 9783642111754
Subject(s): Additional physical formats: 9783642111747 | Buchausg. u.d.T.: Introduction to complex reflection groups and their braid groups. Berlin : Springer, 2010. XI, 138 S.DDC classification:
  • 512.2
MSC: MSC: *20F55 | 20-02 | 20F36 | 51F15 | 13A50 | 57M25RVK: RVK: SI 850LOC classification:
  • QA174-183
  • QA177
DOI: DOI: 10.1007/978-3-642-11175-4Online resources: Summary: Preliminaries -- Prerequisites and Complements in Commutative Algebra -- Polynomial Invariants of Finite Linear Groups -- Finite Reflection Groups in Characteristic Zero -- Eigenspaces and Regular ElementsSummary: 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 groupsPPN: PPN: 1649984243Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-LNM | ZDB-2-SMA | ZDB-2-LNC
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