Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

A self-contained introduction to the representation theory and harmonic analysis of wreath products of finite groups, with examples and exercises.

Tullio Ceccherini-Silberstein (Author), Fabio Scarabotti (Author), Filippo Tolli (Author)

9781107627857, Cambridge University Press

Paperback / softback, published 16 January 2014

176 pages, 5 b/w illus. 2 tables 18 exercises
22.8 x 15.2 x 1 cm, 0.27 kg

This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

Preface
1. General theory
2. Wreath products of finite groups
3. Harmonic analysis on finite wreath products
Bibliography
Index.

Subject Areas: Numerical analysis [PBKS], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB], Groups & group theory [PBG], Algebra [PBF], Mathematics [PB]