The Borel-Weil theorem states that the space of sections of a certain line bundle on the flag variety is isomorphic to the irreducible representation of the corresponding reductive group. The classical result of Demazure describes the restriction of sections to the Schubert subvarieties. These results have analogs for the affine Grassmannian. In the talk, we will recall these constructions and describe their analog for the Beilinson-Drinfeld Grassmannian. The representations, arising in this situation, can be considered as an interesting generalization of global Weyl modules over the current algebra.