Note on duality on polarized symplectic manifolds
type: Item
instance of: scholarly article
title: Note on duality on polarized symplectic manifolds
zbMATH Open document ID: 0602.58023
DOI: 10.1016/0034-4877(84)90043-0
author: Hans R. Fischer
author: Floyd L. Williams
published in: Reports on Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: We use some of our earlier results of [Trans. Am. Math. Soc. 252, 163-195 (1979; Zbl 0423.14008)] to derive a general duality theorem for the cohomologies of foliated structures on a manifold. The result is applied to the special case of symplectic manifold M on which the foliation is given by a complex polarization F in the sense of geometric quantization. We obtain, for example, a rigorous proof of the fact that for a smooth function f on M whose Hamiltonian vector field leaves F invariant, the spectrum of the corresponding prequantization operator v(f) coincides with the spectrum of its transpose, under the above duality. This latter result was obtained by D. J. Simms.
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 58A30
zbMATH DE Number: 3971817
zbMATH Keywords: duality theorem
zbMATH Keywords: cohomologies of foliated structures on a manifold
zbMATH Keywords: geometric quantization
MaRDI profile type: Publication
full work available at URL: 0034-4877(84)90043-0
OpenAlex ID: W1973448340
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description: scientific article; zbMATH DE number 3971817