  We study the $L^2$-boundedness of the Poisson transforms associated to the
homogeneous vector bundles $ Sp(n,1)\times_{Sp(n)\times Sp(1)} V_\tau$ over the
quaternionic hyperbolic spaces $ Sp(n,1)/Sp(n)\times Sp(1)$ associated with
irreducible representations $\tau$ of $ Sp(n)\times Sp(1)$ which are trivial on
$ Sp(n)$. As a consequence, we describe the image of the section space
$L^2(Sp(n,1)\times_{Sp(n)\times Sp(1)} V_\tau)$ under the generalized spectral
projections associated to a family of eigensections of the Casimir operator.
