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 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.
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@misc{ArdThesis,
author={Ardakov, K.},
TITLE={Krull dimension of {I}wasawa algebras and some related topics},
NOTE={Ph.D. thesis, University of Cambridge},
YEAR={2004},
} -
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@article {ArdBro2007, MRKEY = {2272136},
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