Geometric Casselman-Shalika in mixed characteristic
Algebraic Geometry
2024-08-16 v1 Number Theory
Representation Theory
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.
Keywords
Cite
@article{arxiv.2408.07953,
title = {Geometric Casselman-Shalika in mixed characteristic},
author = {Ashwin Iyengar and Milton Lin and Konrad Zou},
journal= {arXiv preprint arXiv:2408.07953},
year = {2024}
}
Comments
50 pages. Comments very welcome!