Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject.

From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

chapter I|43 pages

Borel Spaces and Selection Theorems

chapter II|36 pages

Preliminaries on C* Algebras

chapter III|54 pages

Type One Von Neumann Algebras

chapter IV|58 pages

Groups and Group Actions

chapter V|34 pages

Induced Actions and Representations

chapter VI|38 pages

Dual Topologies

chapter VII|98 pages

Left Hilbert Algebras

chapter VIII|36 pages

The Fourier-Stieltjes Algebra