2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70504We 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.41 pages, 2 figures, computation of cohomology works on any Hermitian symmetric variety of ADE type, the relations are explicitly computed for GrassmanniansAlgebraic GeometryRepresentation Theory14F05; 14M17; 32M15; 16G20text