Group Representations and Non-Commutative Harmonic Analysis with Applications to Analysis, Number Theory, and Physics

George Whitelaw Mackey's Group Representations and Non-Commutative Harmonic Analysis with Applications to Analysis, Number Theory, and Physics stands as a landmark text in mathematics, offering a profound and unified perspective on the interplay between abstract group theory and its concrete applications. Originally developed from Mackey's influential lecture notes, the book provides a comprehensive introduction to the theory of unitary group representations of locally compact groups, a field that Mackey himself pioneered. The book is celebrated for its ambitious scope, weaving together seemingly disparate areas of mathematics and physics. This is not an introductory text. A strong background in abstract algebra, topology, and functional analysis is a prerequisite for navigating its dense and sophisticated content. It is primarily aimed at graduate students and researchers in mathematics and theoretical physics who seek a deep and unified understanding of these interconnected fields. For those interested in analysis, the book delves into the intricacies of non-commutative harmonic analysis, extending the familiar concepts of Fourier analysis to more general settings. In the realm of number theory, Mackey reveals deep connections between group representations and the study of automorphic forms etc..