A canonical dimension estimate for non-split semisimple 𝑝-adic Lie groups

Abstract

We prove that the canonical dimension of an admissible Banach space or a locally analytic representation of an arbitrary semisimple p p -adic Lie group is either zero or at least half the dimension of a non-zero coadjoint orbit. This extends the results of Ardakov, Wadsley, and Schmidt in the split semisimple case.