Jacquet modules of locally analytic representations of p-adic reductive groups I. Construction and first properties

Let G be a reductive group defined over a p-adic local field L, let P be a parabolic subgroup of G with Levi quotient M, and write G:=G(L), P:=P(L), and M:=M(L). In this paper we construct a functor JP from the category of essentially admissible locally analytic G-representations to the category of essentially admissible locally analytic M-representations, which we call the Jacquet module functor attached to P, and which coincides with the usual Jacquet module functor of Casselman W., Introduction to the theory of admissible representations of p-adic reductive groups, unpublished notes distributed by P. Sally, draft dated May 7, 1993. Available electronically at http://www.math.ubc.ca/people/faculty/cass/research.html. 5]] on the subcategory of admissible smooth G-representations. We establish several important properties of this functor.