Geometric quantization and quantum moment maps on coadjoint orbits and K\"ahler-Einstein manifolds

Naichung Conan Leung The Chinese University of Hong Kong Qin Li Southern University of Science and Technology Ziming Nikolas Ma The Chinese University of Hong Kong

Differential Geometry mathscidoc:2010.10001

9 pages, 2020.10
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum observables asymptotically via Toeplitz operators. When there is a Hamiltonian $G$-action on a K\"ahler manifold, there are associated symmetries on both the quantum algebra and representation aspects. We show that in nice cases of coadjoint orbits and K\"ahler-Einstein manifolds, these symmetries are strictly compatible (not only asymptotically).
Geometric quantization, coadjoint orbits, K\"ahler-Einstein manifolds
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@inproceedings{naichung2020geometric,
  title={Geometric quantization and quantum moment maps on coadjoint orbits and K\"ahler-Einstein manifolds},
  author={Naichung Conan Leung, Qin Li, and Ziming Nikolas Ma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201027225925025233721},
  pages={9 pages},
  year={2020},
}
Naichung Conan Leung, Qin Li, and Ziming Nikolas Ma. Geometric quantization and quantum moment maps on coadjoint orbits and K\"ahler-Einstein manifolds. 2020. pp.9 pages. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20201027225925025233721.
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