Quivers and the cohomology of homogeneous vector bundles
Giorgio Ottaviani and Elena Rubei
Source: Duke Math. J. Volume 132, Number 3
(2006), 459-508.
Abstract
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 (introduced by Bondal, Kapranov, and Hille) between the category of homogeneous bundles and the category of representations of a certain quiver ${\cal Q}_X$ with relations. We prove that the relations are the commutative ones on projective spaces, but they involve additional scalars on general Grassmannians. In addition, we introduce moduli spaces of homogeneous bundles
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1143935997
Digital Object Identifier: doi:10.1215/S0012-7094-06-13233-7
Mathematical Reviews number (MathSciNet): MR2219264
Zentralblatt MATH identifier: 05039110
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