A holomorphic representation of the multidimensional Jacobi algebra

Abstract

We present a holomorphic representation of the Jacobi algebra ${\mathfrak{h}}_n⋊\mathfrak{sp}(n,\mathbb{R})$ by first order differential operators with polynomial coefficients on the manifold ${\mathbb{C}}^n\times {\mathcal{D}}_n$. We construct the Hilbert space of holomorphic functions on which these differential operators act.

26 pages, To appear in the Proceedings of the Third Operator Algebras and Mathematical Physics Conference, Bucharest, Romania, August 10 -- 17, 2005, corrected typos

References in corpus (10)

• Holstein-Primakoff/Bogoliubov Transformations and the Multiboson System
• Representations of the Schrodinger algebra and Appell systems
• A holomorphic representation of the multidimensional Jacobi algebra
• A holomorphic representation of the Jacobi algebra
• Realization of coherent state Lie algebras by differential operators
• Coherent state embeddings, polar divisors and Cauchy formulas
• Differential operators on orbits of coherent states
• Finite-dimensional Lie subalgebras of the Weyl algebra
• Geometrical phases on hermitian symmetric spaces
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Cited by in corpus (13)

• A holomorphic representation of the multidimensional Jacobi algebra
• A holomorphic representation of the Jacobi algebra
• A convenient coordinatization of Siegel-Jacobi domains
• Balanced Metric and Berezin Quantization on the Siegel-Jacobi Ball
• On the geometry of Siegel-Jacobi domains
• Bergman representative coordinates on the Siegel-Jacobi disk
• Invariant metric on the extended Siegel-Jacobi upper half space
• The Real Jacobi Group Revisited
• Geodesics associated to the balanced metric on the Siegel-Jacobi ball
• Hamiltonian systems on almost cosymplectic manifolds
• Remarks on the geometry of the extended Siegel--Jacobi upper half-plane
• Geodesics on the extended Siegel-Jacobi upper half-plane
• Wei-Norman and Berezin's equations of motion on the Siegel-Jacobi disk