Dimensions of some locally analytic representations

Abstract

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