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, introduced in citeemerton-jacquet. 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 the construction in of eigenvarieties in citeemerton-interpolation by constructing eigenvarieties interpolating automorphic representations whose local components at $p$ are not necessarily principal series.