On the geometry of Siegel-Jacobi domains

Abstract

We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel-Jacobi disk are obtained. The scalar holomorphic discrete series of the Jacobi group for the Siegel-Jacobi disk is constructed and polynomial orthonormal bases of the representation spaces are given.

15 pages, Latex, AMS fonts, paper presented at the the International Conference "Differential Geometry and Dynamical Systems", August 25-28, 2010, University Politehnica of Bucharest, Romania

References in corpus (3)

• Invariant metrics and Laplacians on Siegel-Jacobi space
• A holomorphic representation of the multidimensional Jacobi algebra
• A holomorphic representation of the Jacobi algebra

Cited by in corpus (5)

• A convenient coordinatization of Siegel-Jacobi domains
• Gaussian distributions, Jacobi group and Siegel-Jacobi space
• Invariant metric on the extended Siegel-Jacobi upper half space
• Coherent states and geometry on the Siegel-Jacobi disk
• Hamiltonian systems on almost cosymplectic manifolds