  Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(KE_4)$
present a challenging example of AdS/CFT correspondence. At present, their
field theory duals for $KE_4=\mathbb{CP}^2$ base are proposed only within a
restricted range $3p/2\le k \le 2p$ as ${\cal N}=2$ quiver Chern-Simons-matter
theories with $SU(N)\times SU(N)\times SU(N)$ gauge group, nine bifundamental
chiral multiplets interacting through a cubic superpotential. To further
elucidate this correspondence, we use particle approximation both at classical
and quantum level. We setup a concrete AdS/CFT mapping of conserved quantities
using geodesic motions, and turn to solutions of scalar Laplace equation in
$Y^{p,k}$. The eigenmodes also provide an interesting subset of Kaluza-Klein
spectrum for $D=11$ supergravity in ${\rm AdS}_4\times Y^{p,k}$, and are dual
to protected operators written in terms of matter multiplets in the dual
conformal field theory.
