## Duke Mathematical Journal

### Quivers and the cohomology of homogeneous vector bundles

#### 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

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

#### Citation

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. http://projecteuclid.org/euclid.dmj/1143935997.

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