Une équivalence de catégories
We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.