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

Author: 

Ardakov, K
Wadsley, S

Publication Date: 

1 September 2013

Journal: 

Annals of Mathematics

Last Updated: 

2019-04-27T17:24:10.48+01:00

Issue: 

2

Volume: 

178

page: 

453-557

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.

Symplectic id: 

399414

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article