Ebook: Noncompact Lie Groups and Some of Their Applications

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.

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Content:
Front Matter....Pages i-xi
Noncompact Lie Groups, their Algebras and some of their Applications....Pages 1-54
Harish-Chandra’s c-Function. A Mathematical Jewel....Pages 55-67
Basic Harmonic Analysis on Pseudo-Riemannian Symmetric Spaces....Pages 69-101
Ordinary- and Momentum-Space Conformal Compactifications: Some Possible Observable Consequences....Pages 103-121
Radon transform on halfplanes via group theory....Pages 123-139
Analytic torsion and automorphic forms....Pages 141-146
Diffusion on Compact Ultrametric Spaces....Pages 147-156
Generalized Square Integrability and Coherent States....Pages 157-167
Maximal Abelian Subgroups of SU(p,q) and Integrable Hamiltonian Systems....Pages 169-180
Path Integrals and Lie Groups....Pages 181-198
Representations of Diffeomorphism Groups and the Infinite Symmetric Group....Pages 199-224
Characters of Lie Groups....Pages 225-237
Weyl Group Actions on Lagrangian Cycles and Rossmann’s Formula....Pages 239-242
Taylor Formula, Tensor Products, and Unitarizability....Pages 243-250
A Connection between Lie Algebra Roots and Weights and the Fock Space Construction....Pages 251-263
Applications of Sp(3,R) in Nuclear Physics....Pages 265-284
Nilpotent Groups and Anharmonic Oscillators....Pages 285-300
Extensions of the Mass 0 Helicity 0 Representation of the Poincare Group....Pages 301-313
Invariant causal propagators in conformal space....Pages 315-324
Gauge groups, anomalies and non-abelian cohomology....Pages 325-331
The E8 Family of Quasicrystals....Pages 333-340
Wavelet Interpolation and Approximate Solutions of Elliptic Partial Differential Equations....Pages 341-347
From Super Lie Algebras to Supergroups: Matrix Realizations and the Factorisation Problem....Pages 349-366
Current Algebras as Hilbert Space Operator Cocycles....Pages 367-372
Non-Linear Realization Technique — The most Convenient Way of Deriving N=1 Supergravity....Pages 373-390
Toda Systems as Constrained Linear Systems....Pages 391-404
Universal T-matrix for Twisted Quantum g?(N)....Pages 405-411
Unitary Representations of Quantum Lorentz Group....Pages 413-422
Contraction of Quantum Groups and Lattice Physics....Pages 423-452
A Quantum Poincar? Group and the Dirac-Coulomb Problem....Pages 453-472
....Pages 473-485