Quivers and the cohomology of homogeneous vector bundles

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dc.creatorOttaviani, Giorgio
dc.creatorRubei, Elena
dc.date2004-03-18
dc.date2005-04-22
dc.date.accessioned2026-07-07T05:06:32Z
dc.date.available2026-07-07T05:06:32Z
dc.descriptionWe 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.
dc.description41 pages, 2 figures, computation of cohomology works on any Hermitian symmetric variety of ADE type, the relations are explicitly computed for Grassmannians
dc.identifierhttps://arxiv.org/abs/math/0403307
dc.identifierhttp://arxiv.org/abs/math/0403307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70504
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14F05; 14M17; 32M15; 16G20
dc.titleQuivers and the cohomology of homogeneous vector bundles
dc.typetext

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