On simplicity and stability of tangent bundles of rational homogeneous varieties

Ada Boralevi (1)

1 Department of Mathematics and Statistics [Texas Tech]

Given a rational homogeneous variety G/P where G is complex simple and of type ADE, we prove that the tangent bundle TG/P is simple, meaning that its only endomorphisms are scalar multiples of the identity. This result combined with Hitchin-Kobayashi correspondence implies stability of the tangent bundle with respect to the anticanonical polarization. Our main tool is the equivalence of categories between homogeneous vector bundles on G/P and finite dimensional representations of a given quiver with relations.

Mots clés: Simplicity; Stability; Quiver Representation; Homogeneous Vector Bundle

Domaines: Théorie des représentations [math.RT]

Ada Boralevi. On simplicity and stability of tangent bundles of rational homogeneous varieties. 2008. ⟨hal-00441343⟩