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" Noncompact Lie Groups and Some of Their Applications "
edited by Elizabeth A. Tanner, Raj Wilson.
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BL
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774790
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b594785
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| Main Entry
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edited by Elizabeth A. Tanner, Raj Wilson.
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Noncompact Lie Groups and Some of Their Applications\ edited by Elizabeth A. Tanner, Raj Wilson.
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| Publication Statement
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Dordrecht : Springer Netherlands : Imprint : Springer, 1994
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| Series Statement
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NATO ASI series., Series C,, Mathematical and physical sciences ;, 429.
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(512 pages)
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| ISBN
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9401044708
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: 9401110786
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: 9789401044707
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: 9789401110785
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| Contents
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1. Noncompact Lie groups, their algebras and some of their applications --; Lie Groups and Lie Algebras --; 2. Harish-Chandra's c-function. A mathematical jewel --; 3. Basic harmonic analysis on pseudo-Riemannian symmetric spaces --; 4. The extensions of space-time. Physics in the 8-dimensional homogeneous space D = SU(2, 2)/K --; 5. Ordinary --; and momentum --; space conformai compactifications: Some possible observable consequences --; 6. Radon transform on halfplanes via group theory --; 7. Analytic torsion and automorphic forms --; 8. Diffusion on compact ultrametric spaces --; 9. Generalized square integrability and coherent states --; 10. Maximal abelian subgroups of SU(p, q) and integrable Hamiltonian systems --; 11. Path integrals and Lie groups --; 12. Representations of diffeomorphism groups and the infinite symmetric group --; 13. Characters of Lie groups --; 14. Weyl group actions on Lagrangian cycles and Rossmann's formula --; 15. Taylor formula, tensor products, and unitarizability --; 16. A connection between Lie algebra roots and weights and the Fock space construction --; 17. Applications of Sp(3,R) in nuclear physics --; 18. Nilpotent groups and anharmonic oscillators --; 19. Extensions of the mass O helicity O representation of the Poincare group --; 20. Invariant causal propagators in conformai space --; 21. Gauge groups, anomalies and non-abelian cohomology --; 22. The E8 family of quasicrystals --; 23. Wavelet interpolation and approximate solutions of elliptic partial differential equations --; Lie Superalgebras and Lie Supergroups --; 24. From super Lie algebras to supergroups: Matrix realizations and the factorisation problem --; 25. Current algebras as Hilbert space operator cocycles --; 26. Non-linear realization technique --; The most convenient way of deriving N = 1 supergravity --; 27. Toda systems as constrained linear systems --; Quantum Groups --; 28. On the definitions of the quantum group Uh(sl(2, k)) and the restricted dual of Uh(sl(n, k)) --; 29. Universal T-matrix for twisted quantum gl(N) --; 30. Unitary representations of quantum Lorentz group --; 31. Contraction of quantum groups and lattice physics --; 32. A quantum Poincaré group and the Dirac-Coulomb problem.
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| Abstract
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This book contains lectures presented by outstanding mathematicians and mathematical physicists at the NATO Advanced Research Workshop on noncompact Lie groups held in San Antonio, Texas in January 1993. It touches almost every important topics in the modern theory of representations of noncompact Lie groups and Lie algebras, Lie supergroups and Lie superalgebras, and quantum groups. It also includes several of the applications of this theory. The articles are exceptionally well written, ranging from expository articles easily accessible to graduate students to research articles for specialists which provide the most recent developments in this field -- some of which are being published for the first time here. The book also provides a coherent and readable introduction which reviews the underlying theory and defines the fundamental and relevant terms for the reader. The text is an outstanding source of material for mathematicians and mathematical physicists who are working or are planning to work in the field of representation theories of Lie groups, Lie supergroups and quantum groups. <br/>
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Algebra.
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Group theory.
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Mathematics.
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Elizabeth A Tanner
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Raj Wilson
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