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 non-zero 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.

Substantial changes to fill in gaps in the exposition

References in corpus (1)

• Localization of modules for a semisimple Lie algebra in prime characteristic

Cited by in corpus (1)

• Non-Archimedean analytic geometry as relative algebraic geometry