Emerton's Jacquet functors for non-Borel parabolic subgroups

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.