منابع مشابه
Homogeneous Vector Bundles
1. Root Space Decompositions 2 2. Weights 5 3. Weyl Group 8 4. Irreducible Representations 11 5. Basic Concepts of Vector Bundles 13 6. Line Bundles 17 7. Curvature 20 7.1. Curvature of tangent bundles 22 7.2. Curvature of line bundles 24 7.3. Levi curvature 25 8. Ampleness Formulas 27 8.1. Ampleness of irreducible bundles 28 8.2. Ampleness of tangent bundles 29 9. Chern Classes 32 9.1. Chern c...
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The notion of quantum group equivariant homogeneous vector bundles on quantum homogeneous spaces is introduced. The category of such quantum vector bundles is shown to be exact, and its Grothendieck group is determined. It is also shown that the algebras of functions on quantum homogeneous spaces are noetherian.
متن کاملQuivers 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...
متن کاملNotes on homogeneous vector bundles over complex flag manifolds
Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset Σ of simple roots of G, and let Eφ be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation φ of P . Using Bott’s theorem, we obtain sufficient conditions on φ in terms of the combinatorial structure of Σ for some cohomology groups of the sheaf of holomorphic sections ...
متن کاملOn the Differential Geometry of Homogeneous Vector Bundles
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 1992
ISSN: 0010-2571,1420-8946
DOI: 10.1007/bf02566515