Quivers and the cohomology of homogeneous vector bundles

Details Quivers and the cohomology of homogeneous vector bundles Quivers and the cohomology of homogeneous vector bundles

2004-03-18

arxiv.org/abs/math/0403307v2

Mathematics

Algebraic Geometry

41 pages, 2 figures, computation of cohomology works on any Hermitian symmetric variety of ADE type, the relations are explici

Scientific paper

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.

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