Meinolf Geck and Götz Pfeiffer,

Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras.

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. The text 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.

London Mathematical Society Monographs 21, Oxford University Press 2000. xvi + 446 pages. ISBN 0-19-850250-8.

Roger W. Carter (Reviewer), Characters of finite Coxeter groups and Iwahori-Hecke algebras by Meinolf Geck and Götz Pfeiffer, Bull. Amer. Math. Soc.