(I apologize in advance for the vagueness of my question). Let $G$ be a reductive algebraic group over $\mathbb C$ with Lie algebra $\frak g$ and Borel $B$. I have seen casual references to the fact that relative Lie algebra cohomology (sometimes also called cohomology of a pair) with coefficients in a $B$-module $V$ is, with the right choice of pair of Lie algebras, related to sheaf cohomology of $G/B$ with coefficients in $V$. Is there a reference for this fact, and is there a precise statement one can make? In particular, which Lie algebras should one use? (My guess would be the pair $(\frak b, \frak h)$, where $\frak b := $ Lie($B$) and $\frak h$ is a Cartan of $\frak b$).



Relative Lie Algebra cohomology and sheaf cohomology
The statement you're looking for is that for a representation $V$ of $G$, the sheaf cohomology of the vector bundle $G\times\_B V$ on $G/B$ coincides with the Lie algebra cohomology for $\mathfrak{b}$ acting on $V$. This goes back to [Kostant](http://scholar.google.com/scholar?cluster=1752913425771819379&hl=en&as_sdt=0,38). 


