Classification of $A_{\mathfrak{q}}(\lambda )$ modules by their Dirac cohomology for type $D$, $G_2$ and $\mathfrak{s}\mathfrak{p}(2n,\mathbb{R})$

Let $G$ be a connected real reductive group with maximal compact subgroup $K$ of the same rank as $G$. In the recent paper of Huang, Pand\v{z}i'{c} and Vogan, it was shown that the admissible $\mathrm{\Theta }$–stable parabolic subalgebras $\mathfrak{q}$ of $\mathfrak{g}$ are in one-to-one correspodence with the faces of $W\rho$ intersecting the $\mathfrak{k}$–dominant Weyl chamber and that $A_{\mathfrak{q}}(0)$–modules can be classified by their Dirac cohomology in geometric terms. They described in detail the cases when ${\mathfrak{g}}_0$ is of type $A$, $B$, $F$ and $C$ except for $\mathfrak{g}0 = \mathfrak{sp}(2n, $\mathbb{R}$)$\mathrm{.}Wewilldescribefacescorrespondingto$A{\mathfrak{q}}(0)$--modulesfor$\mathfrak{g}_0 = \mathfrak{sp}(2n, $\mathbb{R}$)$andfor$\mathfrak{g}_0$oftype$D$and$G_2$.