The Twisted Satake Transform and the Casselman-Shalika Formula for Quasi-Split Groups
- Resource Type
- Working Paper
- Authors
- Gurevich, Nadya; Karasiewicz, Edmund
- Source
- Subject
- Mathematics - Representation Theory
Mathematics - Number Theory
- Language
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.