Noncompact Lie Groups and Some of Their Applications

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. Todasystems 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.