On irreducible representations of compact $p$-adic analytic groups


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.


Konstantin Ardakov

School of Mathematical Sciences, Queen Mary, University of London, MIle End Road, London E1 4NS, United Kingdom

Simon Wadsley

Homerton College, Hills Road, Cambridge CB2 8PH, United Kingdom