Résolutions de Demazure affines et formule de Casselman-Shalika géométrique

Abstract

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.

33 pages, to appear in Journal of Algebraic Geometry

Cited by in corpus (11)

• Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes)
• The Newton stratification on deformations of local G-shtukas
• Local P-shtukas and their relation to global G-shtukas
• Foliations in deformation spaces of local G-shtukas
• Bessel $F$-isocrystals for reductive groups
• Perverse ${\mathbb{F}}_p$-sheaves on the affine Grassmannian
• Perverse sheaves on affine flags and Langlands dual group
• Equidimensionality of convolution morphisms and applications to saturation problems
• Fake degrees for reflection actions on roots
• On the geometry of affine Deligne-Lusztig varieties for quasi-split groups with very special leve
• Geometric Structure of Affine Deligne-Lusztig Varieties for $G{L}_3$