Ja n 20 04 Resolutions of homogeneous bundles on P 2 Giorgio

2 00 5 Resolutions of homogeneous bundles on P 2

Homogeneous bundles on P2 = SL(3)/P can be described by representations of the parabolic subgroup P . In 1966 Ramanan proved that if ρ is an irreducible representation of P then the induced bundle Eρ on P 2 is simple and even stable (see [Ram]). Since P is not a reductive group, there is a lot of indecomposable reducible representations of P and to classify homogeneous bundles on P2 and among t...

Ja n 20 00 BERNSTEIN – GELFAND – GELFAND SEQUENCES

This paper is devoted to the study of geometric structures modeled on homogeneous spaces G/P , where G is a real or complex semisimple Lie group and P ⊂ G is a parabolic subgroup. We use methods from differential geometry and very elementary finite–dimensional representation theory to construct sequences of invariant differential operators for such geometries, both in the smooth and the holomor...

0 v 2 2 7 Ja n 20 04 A possibility to determine the P - parity of the Θ + pentaquark in the pn → Λ 0 Θ + reaction

Quivers and the cohomology of homogeneous vector bundles

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 between the category of homogeneous bundles and the category of representations of a certain quiver QX with relations, whose vertices are the dominant weights of the reductive part of P . T...

ar X iv : a st ro - p h / 04 01 12 2 v 2 1 9 Ja n 20 04 High Energy Gamma - Ray Astronomy

The physics results of high energy γ-ray astronomy are reported, emphasizing recent achievements with ground-based detectors. This includes some of the instrumental developments and latest projects. The fundamental contribution of the field to the question of Cosmic Ray origin is highlighted.