ABSTRACT
This chapter is a survey of some general results about unitary representations of noncompact, non-Abelian groups, together with some discussion of concrete cases. The proofs of many of the theorems in this subject are lengthy and technical and involve ideas beyond the scope of this book. Hence, to a large extent we shall content ourselves with providing definitions and statements of the theorems, together with references to sources where a detailed treatment can be found. (In particular, the “notes and references” for this material are scattered throughout the chapter instead of being collected in a separate section at the end.)
Our principal object of concern is the set of equivalence classes of irreducible unitary representations of a locally compact group G. This set is called the (unitary) dual space of G. As in Chapters 4 and 5,
we denote it by Ĝ, and we denote the equivalence class of an irreducible representation π by [π].
