Using the coherent states attached to the complex Jacobi group—the semi-direct product of the Heisenberg-Weyl group with the real symplectic group—we study some of the properties of coherent states based on the manifold which is the product of the $n$-dimensional complex plane with the Siegel upper half plane.
Stefan Berceanu. "Coherent States Associated to the Jacobi Group—A Variation on a Theme by Erich Kähler." J. Geom. Symmetry Phys. 9 1 - 8, 2007. https://doi.org/10.7546/jgsp-9-2007-1-8