The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups
Representation Theory
2020-12-21 v1 Number Theory
Abstract
We prove the Casselman-Shalika formula for unramified groups over a non-archimedean local field by studying the action of the spherical Hecke algebra on the space of compact spherical Whittaker functions via the twisted Satake transform. This method provides a conceptual explanation of the appearance of characters of a dual group in the Casselman-Shalika formula.
Cite
@article{arxiv.2012.09893,
title = {The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups},
author = {Nadya Gurevich and Edmund Karasiewicz},
journal= {arXiv preprint arXiv:2012.09893},
year = {2020}
}