Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras
Meinolf Geck and Götz Pfeiffer
Price: £97.00 (hardback)
ISBN-13: 978-0-19-850250-0
Publication date: 10 August 2000
464 pages, 18 line illus, 234x160 mm
Series: London Mathematical Society Monographs number 21
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| Reviews |
| - 'An important book ... The authors make full use of recent advances ... The book is both a valuable resource for the expert and good starting point for the beginning researcher in this field ... this is a very fine book which belongs on the shelves of anyone who is interested in the representation theory of Coxeter groups, Iwahori-Hecke algebras and, more generally, the groups of Lie type.' - Zentralblatt MATH
- 'What makes the book especially valuable are the facts that the authors develop the various necessary theories nearly from the scratch ... and that they include the algorithmic theory as well.' - Monatshefte för Mathematick
- 'Written in an engaging and intelligible style ... well structured and clearly printed.' - EMS
- 'It will be a valuable reference for many years to come.' - Bulletin of the LMS
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| Description | | - First systematic treatment of topic. Applications to many areas of current interest: representation of Lie groups, theory of knots and links. Book will provide reference point for future investigations. Includes algorithmic aspects and links to computer algebra systems, like GAP and MAPLE. Topics developed in a pedagogical way, suitable for post-graduate courses or seminars.
| | Finite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are obtained by a certain deformation process. They have applications in the representation theory of groups of Lie type and the theory of knots and links. The aim of this book is to develop the
theory of conjugacy classes and irreducible characters, both for finite Coxeter groups and the associated Iwahori-Hecke algebras. The topics range from classical results to more recent developments and are treated in a coherent and self-contained way. This is the first book which develops these subjects both from a theoretical and an algorithmic point of view in a systematic way. All types of
finite Coxeter groups are covered. |
| Contents |
1.
Cartan matrices and finite Coxeter groups
2.
Parabolic subgroups
3.
Conjugacy classes and special elements
4.
The braid monoid and good elements
5.
Irreducible characters of finite Coxeter groups
6.
Parabolic subgroups and induced characters
7.
Representation theory of symmetric algebras
8.
Iwahori-Hecke algebras
9.
Characters of Iwahori-Hecke alebras
10.
Character values in classical types
11.
Computing character values and generic degrees
Appendix: Tables for the exceptional types
References
Index
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| Authors, editors,
and contributors |
Meinolf Geck, Institut Girard Desargues, Université Claude Bernard, Lyon and
Götz Pfeiffer, Department of Mathematics, National University of Ireland, Galway
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