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Noncompact Lie Groups and Some of Their Applications

  • Book
  • © 1994

Overview

Editors:
  1. Elizabeth A. Tanner

    1. Division of Mathematics, University of Texas, San Antonio, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Raj Wilson

    1. Division of Mathematics, University of Texas, San Antonio, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Nato Science Series C: (ASIC, volume 429)

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Table of contents (32 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Noncompact Lie Groups, their Algebras and some of their Applications

    1. Noncompact Lie Groups, their Algebras and some of their Applications

      • Elizabeth A. Tanner, Raj Wilson
      Pages 1-54

  3. Lie Groups and Lie Algebras

    1. Harish-Chandra’s c-Function. A Mathematical Jewel

      • Sigurdur Helgason
      Pages 55-67

    2. Basic Harmonic Analysis on Pseudo-Riemannian Symmetric Spaces

      • E. Van Den Ban, M. Flensted-Jensen, H. Schlichtkrull
      Pages 69-101

    3. The Extensions of Space-Time. Physics in the 8-dimensional Homogeneous Space D = SU (2,2)/K

      • Asim O. Barut
      Pages 103-121

    4. Ordinary- and Momentum-Space Conformal Compactifications: Some Possible Observable Consequences

      • P. Budinich
      Pages 123-139

    5. Radon transform on halfplanes via group theory

      • Joachim Hilgert
      Pages 141-146

    6. Analytic torsion and automorphic forms

      • Birgit Speh
      Pages 147-156

    7. Diffusion on Compact Ultrametric Spaces

      • A. Figà-Talamanca
      Pages 157-167

    8. Generalized Square Integrability and Coherent States

      • J.-P. Antoine
      Pages 169-180

    9. Maximal Abelian Subgroups of SU(p,q) and Integrable Hamiltonian Systems

      • P. Winternitz, M. A. del Olmo, M. A. Rodríguez
      Pages 181-198

    10. Path Integrals and Lie Groups

      • Akira Inomata, Georg Junker
      Pages 199-224

    11. Representations of Diffeomorphism Groups and the Infinite Symmetric Group

      • Takeshi Hirai
      Pages 225-237

    12. Characters of Lie Groups

      • M. Anoussis
      Pages 239-242

    13. Weyl Group Actions on Lagrangian Cycles and Rossmann’s Formula

      • W. Schmid, K. Vilonen
      Pages 243-250

    14. Taylor Formula, Tensor Products, and Unitarizability

      • Eugene Angelopoulos
      Pages 251-263

    15. A Connection between Lie Algebra Roots and Weights and the Fock Space Construction

      • George W. Mackey
      Pages 265-284

    16. Applications of Sp(3,R) in Nuclear Physics

      • David J. Rowe
      Pages 285-300

    17. Nilpotent Groups and Anharmonic Oscillators

      • W. H. Klink
      Pages 301-313

    18. Extensions of the Mass 0 Helicity 0 Representation of the Poincare Group

      • Charles H. Conley
      Pages 315-324
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Keywords

About this book

During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig­ nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy­ namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.

Editors and Affiliations

  • Division of Mathematics, University of Texas, San Antonio, USA

    Elizabeth A. Tanner, Raj Wilson

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