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Abstract:
The category of homogeneous vector bundles on a flag manifold X=G/P of ADE-type
is equivalent to the category of representations of a certain quiver Q_X with relations.
This equivalence was found in some cases by Bondal, Kapranov and Hille.
In the particular case of Hermitian symmetric varieties, Ottaviani and Rubei used this
equivalence as a tool to compute the cohomology of homogeneous vector bundles, thus
generalizing the well-known Borel-Weil-Bott Theorem to not necessarily irreducible bundles.
I will show results holding in the general case.
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