  Let K be a locally compact nonarchimedean field, g a split reductive Lie
algebra over K and U(g) its universal enveloping algebra. We study the category
C_g of coadmissible modules over the nonarchimedean Arens-Michael envelope of
U(g). Let p be a parabolic subalgebra of g. The main result identifies a
certain explicitly given highest weight category inside C_g with the classical
parabolic BGG category of g relative to p. This paper is in final form,
replaces and expands the former preprint 'BGG reciprocity for p-adic
Arens-Michael envelopes of semisimple Lie algebras' and appears in Journal of
Algebra.
