UNITARY FUNCTORIAL CORRESPONDENCES FOR p−ADIC GROUPS

Abstract. In this paper, we generalize the results of [BM1, BM2] to affine Hecke algebras of arbitrary isogeny class with geometric unequal parameters, and extended by groups of automorphisms of the root datum. When the theory of types ([BK1, BK2]) gives a Hecke algebra of the form considered in this paper, our results establish a transfer of unitarity from the corresponding Bernstein component of the category of smooth representations of p-adic groups to the associated categories of Hecke algebra modules, as well as a unified framework for unitary functorial correspondences between certain Bernstein components of possibly different p-adic groups. Content