Spinc-quantization and the K-multiplicities of the discrete series
Paul-Émile Paradan (2003)
Annales scientifiques de l'École Normale Supérieure
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Paul-Émile Paradan (2003)
Annales scientifiques de l'École Normale Supérieure
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Arturo Echeverría-Enriquez, Miguel C. Muñoz-Lecanda, Narciso Román-Roy, Carles Victoria-Monge (1998)
Extracta Mathematicae
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K. Gawędzki
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CONTENTSI. Introduction............................................................................................................................................... 5II. Preliminary notions................................................................................................................................ 7III. Geometric quantization.........................................................................................................................12 A. Elements of...
Frank Loose (1997)
Annales de l'institut Fourier
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A Liouville form on a symplectic manifold is by definition a potential of the symplectic form . Its center is given by . A normal form for certain Liouville forms in a neighborhood of its center is given.
Alan Weinstein (1993-1994)
Séminaire Bourbaki
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Viktor Ginzburg, Richard Montgomery (2000)
Banach Center Publications
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A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist....
Richard Melrose (2004)
Annales de l’institut Fourier
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The notion of a local line bundle on a manifold, classified by 2-cohomology with real coefficients, is introduced. The twisting of pseudodifferential operators by such a line bundle leads to an algebroid with elliptic elements with real-valued index, given by a twisted variant of the Atiyah-Singer index formula. Using ideas of Boutet de Monvel and Guillemin the corresponding twisted Toeplitz algebroid on any compact symplectic manifold is shown to yield the star...