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The Gelfand-Cetlin system and quantization of the complex flag manifolds. (English) Zbl 0522.58021

MSC:
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
53D50 Geometric quantization
53D20 Momentum maps; symplectic reduction
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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References:
[1] Borel, A; Weil, A, Representations lineaires et espaces homogenes kaehlerians des groupes de Lie compact, (), expose by J.-P. Serre
[2] Duistermaat, J.J, On global action-angle coordinates, Comm. pure appl. math., 33, 687-706, (1980) · Zbl 0439.58014
[3] Guillemin, V; Sternberg, S, The moment map and collective motion, Ann. phys., 127, 220-253, (1980) · Zbl 0453.58015
[4] Guillemin, V; Sternberg, S, Moments and reductions, (), to appear · Zbl 0503.58018
[5] Guillemin, V; Sternberg, S, Geometric quantization and multiplicities of group representations, Inventiones, 67, 515-538, (1982) · Zbl 0503.58018
[6] \scV. Guillemin and S. Sternberg, “On Collective Complete Integrability According to the Method of Thimm,” to appear. · Zbl 0511.58024
[7] Kostant, B, Quantization and unitary representations, (), 87-208
[8] Sniatycki, J, On cohomology groups appearing in geometric quantization, (), 46-66
[9] Thimm, A, Integrable geodesic flows on homogeneous spaces, Ergodic theory and dynamical systems, 1, 495-517, (1980) · Zbl 0491.58014
[10] Weinstein, A, Lectures on symplectic manifolds, () · Zbl 0406.53031
[11] Weinstein, A, Quasi classical mechanics on spheres, (), 25-32
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