Emerton's Jacquet functors for non-Borel parabolic subgroups

Abstract

This paper studies Emerton's Jacquet module functor for locally analytic representations of p-adic reductive groups. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup of M gives rise to essentially admissible locally analytic representations of the torus Z(M), which have a natural interpretation in terms of rigid geometry. We use this to extend Emerton's representation-theoretic construction of eigenvarieties by constructing eigenvarieties interpolating automorphic representations whose local components at p are not necessarily principal series.