Duke Mathematical Journal

Quivers and the cohomology of homogeneous vector bundles

Giorgio Ottaviani and Elena Rubei

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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 QX 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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Duke Math. J., Volume 132, Number 3 (2006), 459-508.

First available in Project Euclid: 1 April 2006

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Zentralblatt MATH identifier

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15] 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 16G20: Representations of quivers and partially ordered sets


Ottaviani, Giorgio; Rubei, Elena. Quivers and the cohomology of homogeneous vector bundles. Duke Math. J. 132 (2006), no. 3, 459--508. doi:10.1215/S0012-7094-06-13233-7. https://projecteuclid.org/euclid.dmj/1143935997

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