We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of the image of spherical and Iwahori-fixed vectors in the unramified principal series for this class of models. We provide an explicit alternator expression for the image of spherical vectors under these functionals in terms of the representation theory of the dual group.
Bibliographical noteFunding Information:
This work was supported by NSF grants DMS-1406238 (Brubaker), DMS-1001079 (Bump), and DMS-1500977 (Friedberg) and NSA grant H98230-13-1-0246 (Friedberg).
© 2016 Elsevier Inc.
- Bessel functional
- Casselman-Shalika formula
- Hecke algebra
- Unique functional
- Universal principal series