Geometric Casselman-Shalika in mixed characteristic
classification
🧮 math.AG
math.NTmath.RT
keywords
casselman-shalikacharacteristicgeometricmixedaffineanalogcoefficientscohomology
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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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