Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras
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Author Description
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.
Menrva's Summary
THE THESIS
This text investigates the structural properties of finite Coxeter groups and their corresponding Iwahori-Hecke algebras through both theoretical and algorithmic frameworks. Authors Meinolf Geck and Götz Pfeiffer provide a systematic examination of conjugacy classes and irreducible characters, bridging classical mathematical results with contemporary computational methods. The work serves as a comprehensive reference for researchers applying these algebraic structures to Lie theory and knot theory.
THE SCOPE MAP
What You Will Find
- Theoretical development of conjugacy classes and irreducible characters for finite Coxeter groups.
- Algorithmic approaches to the representation theory of Iwahori-Hecke algebras.
- Systematic coverage of all types of finite Coxeter groups.
- Applications of deformation processes in the context of Lie algebras and algebraic groups.
THE AUTHORITY PERSPECTIVE
Experts recognize this monograph as a foundational resource for those working at the intersection of algebraic group theory and computational mathematics. Readers frequently note the technical density of the prose, which is tailored for advanced students and researchers in the field of representation theory.
Page Count:
464
Publication Date:
2000-10-12
Publisher:
Oxford University Press
ISBN-10:
0198502508
ISBN-13:
9780198502500
Mathematics
Algebra
Representation Theory
Group Theory
Finite Groups
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