  Let $(X,\omega)$ be an integral symplectic manifold and let $(L,\nabla)$ be a
quantum line bundle, with connection, over $X$ having $\omega$ as curvature.
With this data one can define an induced symplectic manifold $(\widetilde
{X},\omega_{\widetilde {X}})$ where $dim \widetilde {X} = 2 + dim X$. It is
then shown that prequantization on $X$ becomes classical Poisson bracket on
$\widetilde {X}$. We consider the possibility that if $X$ is the coadjoint
orbit of a Lie group $K$ then $\widetilde {X}$ is the coadjoint orbit of some
larger Lie group $G$. We show that this is the case if $G$ is a non-compact
simple Lie group with a finite center and $K$ is the maximal compact subgroup
of $G$. The coadjoint orbit $X$ arises (Borel-Weil) from the action of $K$ on
$\p$ where $\g= \k +\p$ is a Cartan decomposition. Using the Kostant-Sekiguchi
correspondence and a diffeomorphism result of M. Vergne we establish a
symplectic isomorphism $(\widetilde {X},\omega_{\widetilde {X}})\cong
(Z,\omega_Z)$ where $Z$ is a non-zero minimal "nilpotent" coadjoint orbit of
$G$. This is applied to show that the split forms of the 5 exceptional Lie
groups arise symplectically from the symplectic induction of coadjoint orbits
of certain classical groups.
