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

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

2011-02-13

arxiv.org/abs/1102.2606v2

Mathematics

Representation Theory

75 pages, minor corrections made

Scientific paper

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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