A Casselman-Shalika formula for the Shalika model of GL_n
Abstract
Description
The 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 GL_n, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of the method, that was introduced by Y.Hironaka, and in effect reduce many such problems to straightforward calculations on the group.
23 pages. Accepted for publication in the Canadian Journal of Mathematics
23 pages. Accepted for publication in the Canadian Journal of Mathematics