An affine Hecke algebra is
additively the tensor product of a finite dimensional Hecke algebra with the
coordinate ring Θ of a complex torus. In this paper we give explicit formulas
for eigenvectors of Θ in unramified principal series representations of the
reductive p-adic group G associated to ℋ. This leads to new information about
intertwining operators, Jacquet modules and submodules of principal series
representations.