Quantization of compact Riemannian symmetric spaces

Abstract

The phase space of a compact, irreducible, simply connected, Riemannian symmetric space admits a natural family of Kähler polarizations parametrized by the upper half plane $S$. Using this family, geometric quantization, including the half-form correction, produces the field $H^{corr}\to S$ of quantum Hilbert spaces. We show that projective flatness of $H^{corr}$ implies, that the symmetric space must be isometric to a compact Lie group equipped with a biinvariant metric. In the latter case the flatness of $H^{corr}$ was previously established.

Typos corrected and parts of the paper are rewritten to make it more reader friendly, following the suggestions of an anonymous referee. It will appear in J. Geom. and Phys

References in corpus (1)

• Semi-classical properties of geometric quantization with metaplectic correction

Cited by in corpus (2)

• Coherent states for compact Lie groups and their large-N limits
• Fibering polarizations and Mabuchi rays on symmetric spaces of compact type