Summary: ON IRREDUCIBLE REPRESENTATIONS OF COMPACT p­ADIC
ANALYTIC GROUPS
KONSTANTIN ARDAKOV AND SIMON WADSLEY
Abstract. We prove that the canonical dimension of a coadmissible repre­
sentation of a semisimple p­adic Lie group in a p­adic Banach space is either
zero or at least half the dimension of a non­zero coadjoint orbit. To do this we
establish analogues for p­adically completed enveloping algebras of Bernstein's
inequality for modules over Weyl algebras, the Beilinson­Bernstein localisa­
tion theorem and Quillen's Lemma about the endomorphism ring of a simple
module over an enveloping algebra.
Contents
1. Introduction 1
2. Background 7
3. Almost commutative a#noid algebras 12
4. Crystalline di#erential operators on homogeneous spaces 17
5. Deformations, completions and characteristic varieties 23
6. The Beilinson­Bernstein theorem for
#
D #
n,K 31

Source: Ardakov, Konstantin - School of Mathematical Sciences, University of Nottingham

Collections: Mathematics