Resumen de On irreducible representations of compact p -adic analytic groups

Konstantin Ardakov, Simon Wadsley

• 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