Explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.

Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.

Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.

Dedicated to Jacques Carmona, an expert in noncommutative harmonic analysis, the volume presents excellent invited/refereed articles by top notch mathematicians. Topics cover general Lie theory, reductive Lie groups, harmonic analysis and the Langlands program, automorphic forms, and Kontsevich quantization. Good text for researchers and grad students in representation theory.

This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.

This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.

''When I was invited to speak at the conference on the history of analysis given at Rice University [in 1977], I decided that it might be interesting to review the history of mathematics and physics in the last three hundred years or so with heavy emphasis on those parts in which harmonic analysis had played a decisive or at least a major role. I was pleased and somewhat astonished to find how much of both subjects could be included under this rubric ... The picture that gradually emerged as the various details fell into place was one that I found very beautiful, and the process of seeing it do so left me in an almost constant state of euphoria. I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists.'' --from the Preface This volume, containing the paper mentioned above as well as five other reprinted papers by Mackey, presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. A seventh paper, written exclusively for this volume, attempts to unify certain themes that emerged after major discoveries in 1967 and 1968 in the areas of Lie algebras, strong interaction physics, statistical mechanics, and nonlinear partial differential equations--discoveries that may at first glance appear to be independent, but which are in fact deeply interrelated. Information for our distributors: Copublished with the London Mathematical Society beginning with volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.