Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

ISBN-13: 9781107627857 / Angielski / Miękka / 2014 / 176 str.

Tullio Ceccherini-Silberstein;Fabio Scarabotti;Filippo Tolli

Opis

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.

Spis treści

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