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Geometric Quantizations Related To The Laplace Eigenspectra Of Compact Riemannian Symmetric Spaces Via Borel-Weil-Bott Theory, Camilo Montoya

FIU Electronic Theses and Dissertations

The purpose of this thesis is to suggest a geometric relation between the Laplace-Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory using ideas from symplectic geometry and geometric quantization. This is done by associating to each compact Riemannian symmetric space, via Marsden-Weinstein reduction, a generalized flag manifold which covers the space parametrizing all of its maximal totally geodesic tori. In the process we notice a direct relation between the Satake diagram of the symmetric space and the painted Dynkin diagram of its associated flag manifold. We consider in detail the examples of the classical simply-connected …