Let $G$ be the semidirect product $V⋊K$ where $K$ is a semisimple compact connected Lie group acting linearly on a finite-dimensional real vector space $V$. Let $𝒪$ be a coadjoint orbit of $G$ associated by the Kirillov-Kostant method of orbits with a unitary irreducible representation $\pi$ of $G$. We consider the case when the corresponding little group $H$ is the centralizer of a torus of $K$. By dequantizing a suitable realization of $\pi$ on a Hilbert space of functions on ${ℂ}^n$ where $n=dim(K/H)$, we construct a symplectomorphism between...