Noncompact Lie Groups and Some of Their Applications

1. Front Matter

   Pages i-xi

   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

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.

• Analytic torsion
• Group theory
• Lattice
• Lie algebra
• Tensor
• algebra
• cohomology
• differential equation
• group action
• harmonic analysis
• homology
• lie group
• operator
• partial differential equation
• wavelet

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

  Elizabeth A. Tanner, Raj Wilson

Policies and ethics