Locally analytic distributions and p-adic representation theory, with applications to GL_2

Details Locally analytic distributions and p-adic representation theory, with applications to GL_2 Locally analytic distributions and p-adic representation theory, with applications to GL_2

1999-12-09

arxiv.org/abs/math/9912073v1

Mathematics

Number Theory

35 pages

Scientific paper

Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex K-vector spaces. We call the objects of this category "admissible" representations and we establish some of their basic properties. Most importantly we show that (at least when G is compact) the category of admissible representations in our sense can be algebraized; it is faithfully full (anti)-embedded into the category of modules over the locally analytic distribution algebra D(G,K) of G over K. As an application of our theory, we prove the topological irreducibility of generic members of the p-adic principal series of GL(2,Qp).

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