  For any reduced crystallographic root system, we introduce a unitary
representation of the (extended) affine Hecke algebra given by discrete
difference-reflection operators acting in a Hilbert space of complex functions
on the weight lattice. It is shown that the action of the center under this
representation is diagonal on the basis of Macdonald spherical functions. As an
application, we compute an explicit Pieri formula for these spherical
functions.
