Homogeneous bundles and the first eigenvalue of symmetric spaces

Abstract

We prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kaehler metric on a compact Hermitian symmetric spaces of ABCD--type.Comment: Some corrections suggested by the referee. To appear on Annales de l'Institut Fourie