Geodesic
On irreducible representations of compact $p$-adic analytic groups
Konstantin Ardakov1 ; Simon Wadsley2
1 School of Mathematical Sciences, Queen Mary, University of London, MIle End Road, London E1 4NS, United Kingdom
2 Homerton College, Hills Road, Cambridge CB2 8PH, United Kingdom
Annals of mathematics, Tome 178 (2013) no. 2, pp. 453-557.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 nonzero 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.
DOI : 10.4007/annals.2013.178.2.3

Konstantin Ardakov 1 ; Simon Wadsley 2

1 School of Mathematical Sciences, Queen Mary, University of London, MIle End Road, London E1 4NS, United Kingdom
2 Homerton College, Hills Road, Cambridge CB2 8PH, United Kingdom 
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Konstantin Ardakov; Simon Wadsley. On irreducible representations of compact $p$-adic analytic groups. Annals of mathematics, Tome 178 (2013) no. 2, pp. 453-557. doi : 10.4007/annals.2013.178.2.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.2.3/

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