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.

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

• 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