A note on Jacquet functors and ordinary parts - Sorensen, Claus (MATHEMATICA SCANDINAVICA, 2017)
In this note we relate Emerton’s Jacquet functor J_P to his ordinary parts functor Ord _P, by computing the χ-eigenspaces Ord ^χ _P for central characters χ. This fills a small gap in the literature. One consequence is a weak adjunction property for unitary characters χ appearing in J_P, with potential applications to local-global compatibility in the p-adic Langlands program in the ordinary case.