Representations and duality of compact groups

  • Edwin Hewitt
  • Kenneth A. Ross
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 152)


In this chapter, we attempt to do for compact [non-Abelian] groups what we did in Chapter Six for locally compact Abelian groups. The task is a formidable one, and as the reader will see we do not give nearly so much detail about compact groups as we did for locally compact Abelian groups. A basic tool in our study is the Weyl-Peter theorem (27.40), which is the central object of § 27- In § 28, we apply representations of compact groups in several directions and also explore some interesting byways. In § 29, we study the unitary groups and present all the unitary representations of U (2) and D (3). Duality for compact groups is taken up in § 30.


Irreducible Component Compact Group Unitary Representation Compact Abelian Group Irreducible Unitary Representation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • Edwin Hewitt
    • 1
  • Kenneth A. Ross
    • 2
  1. 1.Department of Mathematic GN-50University of WashingtonSeattleUSA
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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