Spectral transfer morphisms for unipotent affine Hecke algebras

Abstract

In this paper we will give a complete classification of the spectral transfer morphisms between the unipotent affine Hecke algebras of the various inner forms of a given quasi-split absolutely simple algebraic group, defined over a non-archimidean local field $\textbf{k}$ and split over an unramified extension of $\textbf{k}$. As an application of these results, the results of [O4] on the spectral correspondences associated with such morphisms and some results of Ciubotaru, Kato and Kato [CKK] we prove a conjecture of Hiraga, Ichino and Ikeda [HII] on the formal degrees and adjoint gamma factors for all unipotent discrete series characters of unramified simple groups of adjoint type defined over $\bf{k}$.