Has there been any serious study of automorphisms of extended affine Hecke algebras? Has anyone determined the automorphism group of say, type A extended affine Hecke algebras? I ask because the Iwahori-Matsumoto involution appears to be related to other interesting aspects of representations of p-adic groups/the geometry of Langlands parameters, as in [1]. Thus, it seems natural to ask if other automorphisms of Hecke algebras have similar geometric manifestations.
A cursory google search only yields [2], where they say "Iwahori-Hecke" but it seems they just mean the "finite" part of the Hecke algebras, not the extended affine Hecke algebras which capture the p-adic representation theory. Though, presumably one could leverage their results to say some about automorphisms of extended affine Hecke algebras.
[1] Fourier transform and the Iwahori-Matsumoto involutions - Evans, Mirkovich \url{https://projecteuclid.org/journals/duke-mathematical-journal/volume-86/issue-3/Fourier-transform-and-the-Iwahori-Matsumoto-involution/10.1215/S0012-7094-97-08613-0.short}
[2] Automorphisms of generic Iwahori-Hecke and integral group rings of finite Coxeter groups, Bleher, Geck, and Kimmerle \url{https://www.sciencedirect.com/science/article/pii/S0021869397971180}