On the dimension of locally analytic representations of semisimple p-adic groups

Details On the dimension of locally analytic representations of semisimple p-adic groups On the dimension of locally analytic representations of semisimple p-adic groups

2011-08-07

arxiv.org/abs/1108.1539v1

Mathematics

Representation Theory

13 pages

Scientific paper

We prove an analogue of a theorem of S.P. Smith on universal enveloping algebras in the context of locally analytic representation theory. Let G be a p-adic Lie group whose Lie algebra is split semisimple. Let r be half the dimension of a minimal co-adjoint orbit. The values of r are well-known. We show that the canonical dimension of any admissible locally analytic G-representation which is not zero-dimensional is at least r. We prove this result by reducing it to an analogous statement for modules over p-adically completed deformations of universal enveloping algebras which was established in a recent preprint by K. Ardakov and S. Wadsley.

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