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Print Price: $360.00

Format:
Hardback
461 pp.
numerous figures and line drawings, 160 mm x 234 mm

ISBN-13:
9780198502500

Publication date:
June 2000

Imprint: OUP UK

Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras

Meinolf Geck and Götz Pfeiffer

Series : London Mathematical Society Monographs, 21

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.

Readership : Students of mathematics (algebra, group theory), from graduate level upwards. Researchers and lecturers in mathematics, in the following areas: algebra, group theory, computational group theory, representation theory.

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 algebras; 10 Character values in classical types; 11 Computing character values and generic degrees; Appendix: Tables for the exceptional types; References

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Meinolf Geck, Professor of Mathematics at the University of Lyon, France. Götz Pfeiffer, Lecturer in Mathematics, National University of Ireland at Galway, Ireland

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Special Features

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.