Geometric Casselman-Shalika in mixed characteristic

Published 15 Aug 2024 in math.AG, math.NT, and math.RT | (2408.07953v1)

Abstract: We establish a geometric analog of the Casselman-Shalika formula for a split connected reductive group over a mixed characteristic local field. In particular, we construct sheaves on the Witt vector affine Grassmannian which geometrize the Fourier coefficients of spherical Hecke operators, and compute their cohomology.

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