Supersingular Hecke modules as Galois representations

Let F be a local field of mixed characteristic (0 , p) , let k be a finite extension of its residue field, let H be the pro-p-Iwahori Hecke k-algebra attached to GL(d+1) (F) for some d >= 1. We construct an exact and fully faithful functor from the category of supersingular H-modules to the category of Gal ((F) over bar /F)-representations over k. More generally, for a certain k-algebra H-# surjecting onto H we define the notion of #-supersingular modules and construct an exact and fully faithful functor from the category of #-supersingular H-#-modules to the category of Gal ((F) over bar /F )-representations over k.