Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Tullio Ceccherini-Silberstein · Fabio Scarabotti · Filippo Tolli

Jan 2014 · London Mathematical Society Lecture Note Series Book 410 · Cambridge University Press

About this ebook

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.

About the author

Tullio Ceccherini-Silberstein is a Professor at the Università del Sannio, Italy.

Fabio Scarabotti is a Professor at Sapienza Università di Roma, Italy.

Filippo Tolli is a Professor at Università Roma Tre, Italy.