  The core polarization effect for the electric quadrupole moment of the
neutron-rich $^{31}$Al, $^{33}$Al and $^{35}$Al isotopes in the vicinity of the
island of inversion are investigated by means of the microscopic
particle-vibration coupling model in which the Skyrme Hartee-Fock-Bogoliubov
and quasiparticle-random-phase approximation are used to calculate the
single-quasiparticle wave functions and the excitation modes. It is found that
the polarization charge for the proton $1d_{5/2}$ hole state in $^{33}$Al is
quite sensitive to coupling to the neutrons in the $pf$-shell associated with
the pairing correlations, and that the polarization charge in $^{35}$Al becomes
larger due to the stronger collectivity of the low-lying quadrupole vibrational
mode in the neighboring $^{36}$Si nucleus.
