Spectral transfer morphisms for affine Hecke algebras

In this talk we introduce the notion of a spectral transfer morphism between affine Hecke algebras. This notion relates to the role affine Hecke algebras play in the harmonic analysis of p-adic reductive groups. Admittedly, the subject of this talk is not immediately related to the main topic of the meeting, hypergeometric functions. It could be mentioned though that affine Hecke algebras play a dominant role in the theory of the so-called hypergeometric functions associated to root systems, a theory in which hypergeometric functions are viewed as generalizations of elementary zonal spherical functions of both real and p-adic reductive groups (Macdonald-Cherednik theory, see e.g. [2], [4], [7], [9]).
The results on spectral transfer morphisms presented in this talk have not yet been published. A publication with complete proofs is in preparation.