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ON IRREDUCIBLE REPRESENTATIONS OF COMPACT p-ADIC ANALYTIC GROUPS
 

Summary: ON IRREDUCIBLE REPRESENTATIONS OF COMPACT p-ADIC
ANALYTIC GROUPS
KONSTANTIN ARDAKOV AND SIMON WADSLEY
Abstract. We prove that the canonical dimension of a coadmissible repre-
sentation 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 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 affinoid algebras 12
4. Crystalline differential operators on homogeneous spaces 17
5. Deformations, completions and characteristic varieties 23
6. The Beilinson-Bernstein theorem for D
n,K 31
7. Bernstein's Inequality 39
8. Quillen's Lemma 42

  

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

 

Collections: Mathematics