R\'esolutions de Demazure affines et formule de Casselman-Shalika   g\'eom\'etrique
  We prove a conjecture of Frenkel, Gaitsgory, Kazhdan and Vilonen, related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a a split reductive group. Our proof is an extension of the proof given by the first author in the case of GL(n) (see math/9801109); it relies on the study of certain resolutions of Schubert varieties in the affine Grassmannian, built from the so-called minuscule or quasi-minuscule cases. 
B.C. Ngo (CNRS, Universit\'e Paris 13), P. Polo (CNRS, Universit\'e   Paris 13)