Translation functors for locally analytic representations

Let G be a p-adic Lie group with reductive Lie algebra [Formula: see text]. In analogy to the translation functors introduced by Bernstein and Gelfand on the categories of [Formula: see text]-modules, we consider similarly defined functors on the category of modules over the locally analytic distribution algebra [Formula: see text] on which the center of [Formula: see text] acts locally finitely. These functors induce equivalences between certain subcategories of the latter category. Furthermore, these translation functors are naturally related to those on category [Formula: see text] via the functors from category [Formula: see text] to the category of coadmissible modules. We also investigate the effect of the translation functors on locally analytic representations [Formula: see text] associated by the p-adic Langlands correspondence for [Formula: see text] to two-dimensional Galois representations V.