2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59110We 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.33 pages, to appear in Journal of Algebraic GeometryAlgebraic Geometrytext