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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

  • Editors
  • J. A. Wolf
  • M. Cahen
  • M. De Wilde

Part of the Mathematical Physics and Applied Mathematics book series (MPAM, volume 5)

Table of contents

  1. Front Matter
    Pages i-viii
  2. General Background

    1. Robert J. Blattner
      Pages 1-67
  3. Foundations of Representation Theory for Semisimple Lie Groups

    1. Front Matter
      Pages 69-70
    2. Joseph A. Wolf
      Pages 71-93
    3. Joseph A. Wolf
      Pages 94-108
    4. Joseph A. Wolf
      Pages 109-130
  4. Infinitesimal Theory of Representations of Semisimple Lie Groups

  5. The Role of Differential Equations in the Plancherel Theorem

  6. A Geometric Construction of the Discrete Series for Semisimple Lie Groups

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

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

  9. Introduction to the 1-Cohomology of Lie Groups

  10. Random Walks on Lie Groups

    1. Harry Furstenberg
      Pages 467-489
  11. Back Matter
    Pages 491-496

About this book

Introduction

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.

Keywords

calculus differential equation fourier analysis harmonic analysis

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-8961-0
  • Copyright Information Springer Science+Business Media B.V. 1980
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-009-8963-4
  • Online ISBN 978-94-009-8961-0
  • Buy this book on publisher's site