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Affine Demazure resolutions and the geometric Casselman-Shalika formula. (Résolutions de Demazure affines et formule de Casselman-Shalika géométrique.) (French) Zbl 1041.14002

Summary: We prove a conjecture of E. Frenkel, D. Gaitsgory, D. Kazhdan and K. Vilonen [J. Am. Math. Soc. 11, 451–484 (1988; Zbl 1068.11501)] which is supported by a paper by W. Casselman and J. Shalika [Compos. Math. 41, 207–231 (1980; Zbl 0472.22005)] related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a split reductive group.

MSC:

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14G15 Finite ground fields in algebraic geometry
14M15 Grassmannians, Schubert varieties, flag manifolds
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