Abstract.
Given a Shimura variety S, associated to a reductive algebraic group G, every finite dimensional representation V of G yields a canonical variation of Hodge structure on S, whose cohomology groups are endowed with a mixed Hodge structure, and hence with a weight filtration. The aim of the talk is to explain results obtained in the case of so-called Hilbert-Siegel varieties, suggesting that the notion of "corank" of the representation V could allow to describe the weight filtration via the interpretation of such cohomology spaces in terms of automorphic forms (generalizations of modular forms, corresponding to the case G=SL2).