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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

  • Book
  • © 1980

Overview

Editors:
  1. J. A. Wolf
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  2. M. Cahen
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  3. M. Wilde
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Part of the book series: Mathematical Physics and Applied Mathematics (MPAM, volume 5)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-viii
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  2. General Background

    1. General Background

      • Robert J. Blattner
      Pages 1-67

  3. Foundations of Representation Theory for Semisimple Lie Groups

    1. Front Matter

      Pages 69-70
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    2. Structure of Semisimple Lie Groups

      • Joseph A. Wolf
      Pages 71-93

    3. Finite-Dimensional Representation Theory

      • Joseph A. Wolf
      Pages 94-108

    4. Infinite-Dimensional Representations

      • Joseph A. Wolf
      Pages 109-130

  4. Infinitesimal Theory of Representations of Semisimple Lie Groups

    1. Infinitesimal Theory of Representations of Semisimple Lie Groups

      • V. S. Varadarajan
      Pages 131-255

  5. The Role of Differential Equations in the Plancherel Theorem

    1. The Role of Differential Equations in the Plancherel Theorem

      • P. C. Trombi
      Pages 257-315

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

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

      • Michael Atiyah, Wilfried Schmid
      Pages 317-378

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

    1. Front Matter

      Pages 385-386
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    2. 1-Differentiable Deformations of the Poisson Bracket Lie Algebra

      • M. Flato, D. Sternheimer
      Pages 387-396

    3. Differentiable Deformations of the Poisson Bracket Lie Algebra

      • M. Flato, D. Sternheimer
      Pages 397-407

    4. Physical Applications Related to 1-Differentiable Deformations of Poisson Brackets

      • M. Flato, D. Sternheimer
      Pages 408-418

    5. Physical Applications Related to Differentiable Deformations of Poisson Brackets: Quantum Mechanics

      • M. Flato, D. Sternheimer
      Pages 419-428

    6. Separate and Joint Analyticity of Vectors in Group Representations and an Application to Field Theory

      • M. Flato, D. Sternheimer
      Pages 429-438

    7. Nonlinear Representations of Lie Groups and Applications

      • M. Flato, D. Sternheimer
      Pages 439-448

  8. Introduction to the 1-Cohomology of Lie Groups

    1. Introduction to the 1-Cohomology of Lie Groups

      • Jacques Simon
      Pages 449-465

  9. Random Walks on Lie Groups

    1. Random Walks on Lie Groups

      • Harry Furstenberg
      Pages 467-489

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

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

      • Michael Atiyah, Wilfried Schmid
      Pages 379-383

  11. Back Matter

    Pages 491-496
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Keywords

About this book

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.

Bibliographic Information

  • 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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