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Induced Representations

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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL,volume 198)

Abstract

This chapter contains the basic theory of induced representations of locally compact groups and some more advanced material on this subject. The theory of induced representations of finite groups was extended to locally compact groups by a single person, George Mackey. His basic definition is given in Section 2 and his main results are proved in Sections 8, 9, 10 and 11. Mackey had to restrict himself to separable Hilbert spaces and groups G satisfying the second axiom of countability. For the sake of clarity we shall define induced representations first in this special case. Later in Section 4 we extend Mackey’s definition to arbitrary G and The theorems given in Sections 8, 9, 10 and 11 are proved in full generality.

Keywords

  • Hilbert Space
  • Tensor Product
  • Invariant Measure
  • Compact Group
  • Unitary Representation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-80741-1_6
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© 1973 Springer-Verlag Berlin Heidelberg

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Gaal, S.A. (1973). Induced Representations. In: Linear Analysis and Representation Theory. Die Grundlehren der mathematischen Wissenschaften, vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80741-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-80741-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-80743-5

  • Online ISBN: 978-3-642-80741-1

  • eBook Packages: Springer Book Archive