On irreducible representations of compact p -adic analytic groups

• Autores: Konstantin Ardakov, Simon Wadsley
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 178, Nº 2, 2013, págs. 453-557
• Idioma: inglés
• DOI: 10.4007/annals.2013.178.2.3
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• Resumen

  • 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