A Casselman–Shalika Formula for the Shalika Model of GLn

Abstract

AbstractThe Casselman–Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of p-adic groups that are associated to unique models (i.e., multiplicity-free induced representations). We apply this method to the case of the Shalika model of GLn, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of themethod, that was introduced by Y.Hironaka, and in effect reducemany such problems to straightforward calculations on the group.