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In the framework of Algebraic Geometry there is the equivalence (introduced by Bondal, Kapranov, and Hille) between the category of homogeneous bundles $E$ on any Hermitian symmetric variety $X=G/P$ of ADE-type and the category of representations of a certain quiver $\mathcal{Q}_X$ with relations.

This allows in some cases the computation of the cohomology groups of such bundles.

See for instance the paper by Ottaviani and Rubei Quivers and the cohomology of homogeneous vector bundles, Duke Mathematical Journal Volume 132, Number 3 (2006), 459-508, and the references given there.

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In the framework of Algebraic Geometry there is the equivalence (introduced by Bondal, Kapranov, and Hille) between the category of homogeneous bundles $E$ on any Hermitian symmetric variety $X=G/P$ of ADE-type and the category of representations of a certain quiver $\mathcal{Q}_X$ with relations.

This allows in some cases the computation of the cohomology groups of such bundles.

See for instance the paper by Ottaviani and Rubei Quivers and the cohomology of homogeneous vector bundles, Duke Mathematical Journal Volume 132, Number 3 (2006), 459-508.