A generalized Casselman-Shalika formula on GL_N

摘要

1. Introduction Let G be the group of F-points of a quasi-split reductive group defined over a nonarchimedean local field F. In developing the theory of Automorphic forms, generic representations play an important role. These are a class of representations which can be realized on the space of Whittaker functions. In particular, the multiplicity one property of Whittaker models implies that any nonzero element in the Whittaker model of a given generic irreducible representation characterizes the representation itself.