Duke Mathematical Journal

Quivers and the cohomology of homogeneous vector bundles

Giorgio Ottaviani and Elena Rubei

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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

Article information

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

Dates
First available in Project Euclid: 1 April 2006

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

Subjects
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

Citation

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


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