Representations and duality of compact groups
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.