  Let $\mathfrak{g}$ be a simple complex Lie algebra of classical type with a
Cartan subalgebra $\mathfrak{h}$. We fix a standard parabolic subalgebra
$\mathfrak{p}\supset \mathfrak{h}$. The socular simple modules are just those
highest weight modules with largest possible Gelfand-Kirillov dimension in the
corresponding parabolic category $\mathcal{O}^{\mathfrak{p}}$. In this article,
we will give an explicit characterization for these modules. When the module is
integral, our characterization is given by the information of the corresponding
Young tableau associated to the given highest weight module. When the module is
nonintegral, we still have some characterization by using the results in the
integral case. In our characterization, we define a particular Young diagram
called Z-diagram. From this diagram, we can describe the partition type of the
unique Richardson orbit associated to the given parabolic subalgebra
$\mathfrak{p}$.
