  We study the Wakimoto modules over the affine Kac-Moody algebras at the
critical level from the point of view of the equivalences of categories
proposed in our previous works, relating categories of representations and
certain categories of sheaves. In particular, we describe explicitly geometric
realizations of the Wakimoto modules as Hecke eigen-D-modules on the affine
Grassmannian and as quasi-coherent sheaves on the flag variety of the Langlands
dual group.
