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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} andVogan, it was shown that the admissible $\Theta$--stable parabolic subalgebras$\mathfrak{q}$ of $\mathfrak{g}$ are in one-to-one correspodence with the facesof $W \rho$ intersecting the $\mathfrak{k}$--dominant Weyl chamber and that$A_{\mathfrak{q}}(0)$--modules can be classified by their Dirac cohomology ingeometric terms. They described in detail the cases when $\mathfrak{g}_0$ is oftype $A$, $B$, $F$ and $C$ except for $\mathfrak{g}_0 = \mathfrak{sp}(2n,\mathbb{R})$. We will describe faces corresponding to$A_{\mathfrak{q}}(0)$--modules for $\mathfrak{g}_0 = \mathfrak{sp}(2n,\mathbb{R})$ and for $\mathfrak{g}_0$ of type $D$ and $G_2$.

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