Abstract
Let ℍn, n ≥ 1, be the (2n+1)-dimensional Heisenberg group and let K be a closed connected subgroup of the unitary group U(n) acting on ℍn by automorphisms. Using the moment map, we provide in this paper a dequantization procedure for all generic admissible coadjoint orbits of the semidirect product G = K ⋉ ℍn. In the opposite direction, we show that Gilmore-Perelomov's coherent states define “pure state quantizations” of such orbits.
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