Vogan's globalization conjecture for nilradical cohomology

Let $\mathfrak{p}$ be a very nice parabolic subalgebra with associated Levi subgroup $L_{0}$, stable Levi factor $\mathfrak{l}$, and nilradical $\mathfrak{n}$. Let $M$ be a Harish-Chandra module for $(\mathfrak{g},K_{0})$, and let $M_{\mathrm{glob}}$ be one of its four canonical globalizations. The $\mathfrak{n}$-cohomology groups $H^{p}(\mathfrak{n},M_{\mathrm{glob}})$ carry their induced topologies, while $H^{p}(\mathfrak{n},M)$ is a Harish-Chandra module for $(\mathfrak{l},K_{0}\cap L_{0})$. Vogan's conjecture. The induced topologies on $H^{p}(\mathfrak{n},M_{\mathrm{glob}})$ are Hausdorff, and there are natural isomorphisms of $L_{0}$-representations

$$H^{p}(\mathfrak{n},M_{\mathrm{glob}})\cong H^{p}(\mathfrak{n},M)_{\mathrm{glob}},$$

where $H^{p}(\mathfrak{n},M)_{\mathrm{glob}}$ denotes the canonical globalization to $L_{0}$ of the Harish-Chandra module $H^{p}(\mathfrak{n},M)$. The conjecture asserts compatibility between the four canonical globalization functors and nilradical cohomology for very nice parabolic subalgebras. Its resolution status is not specified in the supplied text.