Unitary representations of affine Hecke algebras related to Macdonald   spherical functions
  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. 
J. F. van Diejen, E. Emsiz
math.RT math-ph math.MP