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Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups by Filippo Tolli, Fabio Scarabotti, Tullio Ceccherini-Silberstein

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Wreath products of finite groups and their representation theory

In this chapter, which constitutes the core of the book, we develop the representation theory of wreath products. Our exposition is inspired by the monographs of James and Kerber [38] and Huppert [35]. Howewer, our approach is more analytical and, in particular, we interpret the exponentiation and the composition actions in terms of actions on suitable rooted trees. This is done in Section 2.1.2. In Section 2.3 we describe the conjugacy classes of wreath products FG, with particular emphasis on groups of the form C2G (Section 2.3.2), and FSn (Section 2.3.3), and then in Section 2.4 we use the little group method (Theorem 1.3.11) to determine a complete list of irreducible ...

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