Dimensions of some locally analytic representations

Abstract

Let G G be the group of points of a split reductive group over a finite extension of Q p \mathbb {Q}_p . In this paper, we compute the dimensions of certain classes of locally analytic G G -representations. This includes principal series representations and certain representations coming from homogeneous line bundles on p p -adic symmetric spaces. As an application, we compute the dimensions of the unitary GL 2 ( Q p ) \textrm {GL}_2(\mathbb {Q}_p) -representations appearing in Colmez’ p p -adic local Langlands correspondence.