- 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.
- Publisher copy:
- 10.4007/annals.2013.178.2.3
-
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- Journal:
- Annals of Mathematics
- Volume:
- 178
- Issue:
- 2
- Pages:
- 453-557
- Publication date:
- 2011-02-13
- DOI:
- ISSN:
-
0003-486X
- URN:
-
uuid:d143cfc5-8b9f-494e-ae9a-19e0f91ffe04
- Source identifiers:
-
399414
- Local pid:
- pubs:399414
- Copyright date:
- 2011
- Notes:
- Substantial changes to fill in gaps in the exposition
Journal article
On irreducible representations of compact $p$-adic analytic groups
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