Gueo Grantcharov. Relations between Laplace spectra and geometric quantizaton...
Научный Семинар Лаборатории алгебраической геометрии и ее приложений 18.10.19 Gueo Grantcharov (FIU). Relations between Laplace spectra and geometric quantizaton of Riemannian symmetric spaces In a joint work with Dimitar Grantcharov we applied a modified Kostant-Souriau geometric quantization scheme due to and Czyz-Hess to the cotangent bundles of compact rank-one Riemannian symmetric spaces (CROSS). It turns out that the energy spectrum obtained from the quantization is related to the spectrum of the Laplace-Beltrami operator of the CROSS. Moreover, the real dimensions of the corresponding eigenspaces coincide with the complex dimensions of the spaces of holomorphic sections of the quantum bundles. In the talk I'll explain the construction, as well as its extension to the Riemannian symmetric spaces of arbitrary rank.
Научный Семинар Лаборатории алгебраической геометрии и ее приложений 18.10.19 Gueo Grantcharov (FIU). Relations between Laplace spectra and geometric quantizaton of Riemannian symmetric spaces In a joint work with Dimitar Grantcharov we applied a modified Kostant-Souriau geometric quantization scheme due to and Czyz-Hess to the cotangent bundles of compact rank-one Riemannian symmetric spaces (CROSS). It turns out that the energy spectrum obtained from the quantization is related to the spectrum of the Laplace-Beltrami operator of the CROSS. Moreover, the real dimensions of the corresponding eigenspaces coincide with the complex dimensions of the spaces of holomorphic sections of the quantum bundles. In the talk I'll explain the construction, as well as its extension to the Riemannian symmetric spaces of arbitrary rank.