This book presents the text of the lectures which were given at the NATO Advanced Study Institute on Representations of Lie groups and Harmonic Analysis which was held in Liege from September 5 to September 17, 1977. The general aim of this Summer School was to give a coordinated intro duction to the theory of representations of semisimple Lie groups and to non-commutative harmonic analysis on these groups, together with some glance at physical applications and at the related subject of random walks. As will appear to the reader, the order of the papers - which follows relatively closely the order of the lectures which were actually give- follows a logical pattern. The two first papers are introductory: the one by R. Blattner describes in a very progressive way a path going from standard Fourier analysis on IR" to non-commutative harmonic analysis on a locally compact group; the paper by J. Wolf describes the structure of semisimple Lie groups, the finite-dimensional representations of these groups and introduces basic facts about infinite-dimensional unitary representations. Two of the editors want to thank particularly these two lecturers who were very careful to pave the way for the later lectures. Both these chapters give also very useful guidelines to the relevant literature.

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Book Title: Harmonic Analysis and Representations of Semisimple Lie Groups
Book Subtitle: Lectures given at the NATO Advanced Study Institute on Representations of Lie Groups and Harmonic Analysis, held at Liège, Belgium, September 5–17, 1977
Editors: J. A. Wolf, M. Cahen, M. Wilde
Series Title: Mathematical Physics and Applied Mathematics
DOI: https://doi.org/10.1007/978-94-009-8961-0
Publisher: Springer Dordrecht
eBook Packages: Springer Book Archive
Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1980
Hardcover ISBN: 978-90-277-1042-0Published: 31 July 1980
eBook ISBN: 978-94-009-8961-0Published: 06 December 2012
Edition Number: 1
Number of Pages: VIII, 496
Topics: Theoretical, Mathematical and Computational Physics, Abstract Harmonic Analysis

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Table of contents (16 chapters)

Front Matter

General Background

Foundations of Representation Theory for Semisimple Lie Groups

Front Matter

Infinitesimal Theory of Representations of Semisimple Lie Groups

The Role of Differential Equations in the Plancherel Theorem

A Geometric Construction of the Discrete Series for Semisimple Lie Groups

Deformations of Poisson Brackets, Separate and Joint Analyticity in Goup Representations, Nonlinear Group Representations and Physical Applications

Front Matter

Introduction to the 1-Cohomology of Lie Groups

Random Walks on Lie Groups

Erratum to the Paper: A Geometric Construction of the Discrete Series for Semisimple Lie Groups

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