Journal article

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

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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Publisher copy:
10.4007/annals.2013.178.2.3

Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Annals of Mathematics
Volume:
178
Issue:
2
Pages:
453-557
Publication date:
2011-02-13
DOI:
ISSN:
0003-486X
Source identifiers:
399414
Language:
English
Keywords:
Pubs id:
pubs:399414
UUID:
uuid:d143cfc5-8b9f-494e-ae9a-19e0f91ffe04
Local pid:
pubs:399414
Deposit date:
2013-11-16