A holomorphic representation of the Jacobi algebra

Abstract

A representation of the Jacobi algebra ${\mathfrak{h}}_1⋊\mathfrak{su}(1,1)$ by first order differential operators with polynomial coefficients on the manifold $\mathbb{C}\times {\mathcal{D}}_1$ is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.

34 pages, corrected typos in accord with the printed version and the Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI: 10.1142/S0129055X12920018, references updated

References in corpus (7)

• A holomorphic representation of the multidimensional Jacobi algebra
• A holomorphic representation of the Jacobi algebra
• Realization of coherent state Lie algebras by differential operators
• Differential operators on orbits of coherent states
• Finite-dimensional Lie subalgebras of the Weyl algebra
• Geometrical phases on hermitian symmetric spaces
• Linear Hamiltonians on homogeneous Kähler manifolds of coherent states

Cited by in corpus (13)

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• A holomorphic representation of the Jacobi algebra
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• 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