Hi,


Let $G$ be an algebraic reductive group over an algebraically closed field $k$, $T$ a maximal torus and $B = TU$ a Borel subgroup containing it. I'm interested in computing $H^\*(G/U,\mathcal O\_{G/U})$ [corrected typo; I had written $B/U$] (coherent cohomology) (in terms of the representation theory of $G$?). I suppose this is well known, but I can't find it anywhere....


Any suggestions?


Thanks!



Coherent cohomology of G/U, G = reductive group, B = TU Borel subgroup
Assuming that unknown means $G/U$, $H^{\*}(G/U,\mathcal{O}\_{G/U})$ has been computed as a $D\_{G/U}$-module by Levasseur: "Differential operators on the base affine space". The global sections are identified with a certain quotient of global differential operators and the $i$th cohomology is given as a sum of simple $D\_{G/U}(G/U)$-modules indexed by elements of length $i$ in the Weyl group.


