Harmonic Analysis and Representations of Semisimple Lie Groups

Lectures given at the NATO Advanced Study Institute on Representations of Lie Groups and Harmonic Analysis, held at Liège, Belgium, September 5–17, 1977

J.A. Wolf, M. Cahen, M. de Wilde (Herausgeber)

Buch | Hardcover

496 Seiten

1980
Kluwer Academic Publishers (Verlag)
978-90-277-1042-0 (ISBN)

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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.

General Background.- Foundations of Representation Theory for Semisimple Lie Groups.- 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.- Erratum to the Paper: A Geometric Construction of the Discrete Series for Semisimple Lie Groups.- Deformations of Poisson Brackets. Separate and Joint Analyticity in Group Representations. Non-linear Group Representations and Physical Applications.- to the 1-Cohomology of Lie Groups.- Random Walks on Lie Groups.

Erscheint lt. Verlag	31.7.1980
Reihe/Serie	Mathematical Physics and Applied Mathematics ; 5
Zusatzinfo	VIII, 496 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
ISBN-10	90-277-1042-2 / 9027710422
ISBN-13	978-90-277-1042-0 / 9789027710420
Zustand	Neuware