The Jordan-Hölder series of the locally analytic Steinberg representation

Abstract

We determine the composition factors of a Jordan-Hölder series including multiplicities of the locally analytic Steinberg representation. For this purpose, we prove the acyclicity of the evaluated locally analytic Tits complex giving rise to the Steinberg representation. Further we describe some analogue of the Jacquet functor applied to the irreducible principal series representation constructed in citeOS2.