Let $\mathfrak{g}$ a semisimple Lie algebra, $M$ finite-dimensional $\mathfrak{g}-$module, $\mu\in\mathfrak{h}^*_{\mathbb{Z}}$ and $s_i$ simple reflection such that $\langle\mu+\rho,\alpha_i^{\vee}\rangle\ge 0$. I want to determinate $H^p(\mathfrak{n},M)_{\mu}$.
Using Hochchild-Serre spectral sequence for the pair $(\mathfrak{n},\mathfrak{u}_i)$ I can proof that $$H^0(\mathfrak{n}/\mathfrak{u}_i,H^0(\mathfrak{u}_i,M))\simeq H^0{(\mathfrak{n},M)}$$ $$ H^0(\mathfrak{n}/\mathfrak{u}_i,H^1(\mathfrak{u}_i,M))\simeq H^1{(\mathfrak{n},M)}$$ and the other cohomology are zero. What do I say anymore?