  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.
