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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Häftad, Engelska, 2014

AvTullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli,Italy) Ceccherini-Silberstein, Tullio (Universita degli Studi del Sannio,Italy) Scarabotti, Fabio (Universita degli Studi di Roma 'La Sapienza',Filippo (Universita degli Studi Roma Tre) Tolli

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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.

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