Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli

• Publisher: Cambridge University Press
• Year: 2014
• Print ISBN: 9781107627857
• eBook ISBN: 9781107723535
• Topic: Mathématiques
• Subtopic: Algèbre abstraite

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.

Table of contents

• Cover
• Series Page
• Title Page
• Imprints
• Dedication
• Contents
• Preface
• 1 General theory
• 2 Wreath products of finite groups and their representation theory
• 3 Harmonic analysis on some homogeneous spaces of finite wreath products
• References
• Index