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

Ardakov, K

1 September 2013

## Journal:

Annals of Mathematics

## Last Updated:

2020-01-04T10:47:00.84+00:00

2

178

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.

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