Twisted Satake Transform and the Casselman–Shalika Formula for Quasi-Split Groups.
- Resource Type
- Article
- Authors
- Gurevich, Nadya; Karasiewicz, Edmund
- Source
- IMRN: International Mathematics Research Notices. Jul2022, Vol. 2022 Issue 14, p11148-11179. 32p.
- Subject
- *WHITTAKER functions
*HECKE algebras
*SPHERICAL functions
*ARCHIMEDEAN property
*QUASI-Newton methods
- Language
- ISSN
- 1073-7928
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. [ABSTRACT FROM AUTHOR]