Coherent state transforms and abelian varieties

DOI10.1006/jfan.2001.3903zbMath1119.22301OpenAlexW2054997093MaRDI QIDQ1849053

José M. Mourão, Carlos A. A. Florentino, João Pedro Vidal Nunes

Publication date: 28 November 2002

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2001.3903

zbMATH Keywords

Geometric quantizationBlattner-Kostant-Sternberg pairingCoherent state transform for Lie groups

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Coherent states (81R30) Theta functions and abelian varieties (14K25) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items

Degenerating Kähler structures and geometric quantization, Quantization of some moduli spaces of parabolic vector bundles on \({\mathbb C}{\mathbb P}^1\), Coherent state transforms and vector bundles on elliptic curves., Coherent state transform for Landau levels on quasi-tori, Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform, Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties, The complex-time Segal-Bargmann transform, The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Groupe de Picard des variétés de modules de fibrés semi-stable sur les courbes algébriques. (Picard groups of moduli varieties of semi- stable bundles on algebraic curves)
• Mathematical characterization of the physical vacuum for a linear Bose- Einstein field
• Geometric quantization of Chern-Simons gauge theory
• Tata lectures on theta. III
• Yang-Mills theory and the Segal-Bargmann transform
• The Segal-Bargmann ``coherent state transform for compact Lie groups
• Coherent state transforms for spaces of connections
• Stable and unitary vector bundles on a compact Riemann surface
• On Bohr-Sommerfeld bases
• Gauge field theory coherent states (GCS): I. General properties
• REMARKS ON A HILBERT SPACE OF ANALYTIC FUNCTIONS
• Vector bundles on curves and generalized theta functions: recent results and open problems
• Schottky uniformization and vector bundles over Riemann surfaces