  We describe the cohomology groups of a homogeneous vector bundle $E$ on any
Hermitian symmetric variety $X=G/P$ of ADE type as the cohomology of a complex
explicitly described. The main tool is the equivalence between the category of
homogeneous bundles and the category of representations of a certain quiver
${\cal Q}_X$ with relations, whose vertices are the dominant weights of the
reductive part of $P$. This equivalence was found in some cases by Bondal,
Kapranov and Hille and we find the appropriate relations for any Hermitian
symmetric variety, computing them explicitly for Grassmannians.
