Geometric quantization and quantum moment maps on coadjoint orbits and Kähler-Einstein manifolds

Abstract

Deformation quantization and geometric quantization on Kähler 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 Kähler manifold, there are associated symmetries on both the quantum algebra and representation aspects. We show that in nice cases of coadjoint orbits and Kähler-Einstein manifolds, these symmetries are strictly compatible (not only asymptotically).

arXiv comment9 pages, comments are welcome

References in corpus (5)

• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Berezin-Toeplitz quantization on Kaehler manifolds
• Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
• Kapranov's $L_{\infty }$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds
• Bargmann-Fock sheaves on Kähler manifolds