Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras

by Meinolf Geck, Gïtz Pfeiffer

Overview

Finite Coxeter groups and related structures arise naturally in several branches of mathematics such as the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are then obtained by a certain deformation process which have applications in the representation theory of groups of Lie type and the theory of knots and links. This book develops the theory of conjugacy classes and irreducible character, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. Topics covered range from classical results to more recent developments and are clear and concise. This is the first book to develop these subjects both from a theoretical and an algorithmic point of view in a systematic way, covering all types of finite Coxeter groups.

Product Details

ISBN-13:	9780198502500
Publisher:	Oxford University Press
Publication date:	10/12/2000
Series:	London Mathematical Society Monographs , #21
Pages:	461
Product dimensions:	9.21(w) x 6.14(h) x 1.00(d)

About the Author

Universite Claude Bernard, Lyon

National University of Ireland, Galway

Table of Contents

1. Cartan matrices and finite Coxeter groups2. Parabolic subgroups3. Conjugacy classes and special elements4. The braid monoid and good elements5. Irreducible characters of finite Coxeter groups6. Parabolic subgroups and induced characters7. Representation theory of symmetric algebras8. Iwahori-Hecke algebras9. Characters of Iwahori-Hecke alebras10. Character values in classical types11. Computing character values and generic degreesAppendix: Tables for the exceptional typesReferencesIndex

Editorial Reviews

"The contents of the book are well organized ... the chapters can be read independently of each other."—Mathematical Reviews

From the Publisher

Geck (U. Claude Bernard Lyon I, France) and Pfeiffer (mathematics, National U. of Ireland, Galway) develop a substantial part of the theory of conjugacy classes and irreducible characters, both for finite Coxeter groups and for the associated Iwahori-Hecke algebras, systematically covering all types of finite Coxeter groups according to the classification. More specifically, they construct a frame within which to treat such topics as the classification of the conjugacy classes, and the existence of elements with special properties in the classes. They assume readers to be familiar with finite groups, associative algebras, and character theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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