On irreducible representations of compact p-adic analytic groups

Abstract

We prove that the canonical dimension of a coadmissible representation of a semisimple p-adic Lie group in a p-adic Banach space is either zero or at least half the dimension of a nonzero coadjoint orbit. To do this we establish analogues for p-adically completed enveloping algebras of Bernstein’s inequality for modules over Weyl algebras, the Beilinson-Bernstein localisation theorem and Quillen’s Lemma about the endomorphism ring of a simple module over an enveloping algebra.