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Vanishing theorems on cohomology associated to hermitian symmetric spaces

Shingo Murakami (1987)

Annales de l'institut Fourier

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.

Vector fields on the Sato Grassmannian.

Francisco J. Plaza Martín (2005)

Collectanea Mathematica

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.

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