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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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1

General theory

In this chapter we discuss the notion of an induced representation and the structure of the commutant of a representation, and we present a new approach to Clifford theory. We assume the reader to be familiar with the basic rudiments of the representation theory of finite groups. We refer to the monographs by Bump [7], Fulton and Harris [29], Isaacs [36], Serre [67], Simon [68] and Sternberg [73] as basic references; see also our monograph [15].

In Section 1.1 we present the main properties of induction, focusing on the Frobenius character formula and Frobenius reciprocity. Then, in Section 1.2, we discuss several aspects of Frobenius reciprocity for a permutation representation; in particular, we show that the spherical Fourier ...

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