On the geometry of Siegel-Jacobi domains

Details On the geometry of Siegel-Jacobi domains On the geometry of Siegel-Jacobi domains

2010-11-15

arxiv.org/abs/1011.3317v1

Mathematics

Differential Geometry

15 pages, Latex, AMS fonts, paper presented at the the International Conference "Differential Geometry and Dynamical Systems",

Scientific paper

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.

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