Analytic vectors in continuous p-adic representations

Abstract

Given a compact p-adic Lie group G over a finite unramified extension L/Q_p let G_0 be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic G_0-representations that coincides with passage to analytic vectors in case L=Q_p. On the other hand, we study the functor "passage to analytic vectors" and its derived functors over general basefields. As an application we determine the higher analytic vectors in certain locally analytic induced representations.

Final version (appeared in Comp. Math. 2009). Exposition shortened. Minor items corrected

References in corpus (3)

• Algebras of p-adic distributions and admissible representations
• Locally analytic distributions and p-adic representation theory, with applications to GL_2
• U(g)-finite locally analytic representations

Cited by in corpus (5)

• On the Breuil-Mézard conjecture
• Characters of locally analytic representations of p-adic reductive groups
• D-modules on rigid analytic spaces I
• On locally analytic Beilinson-Bernstein localization and the canonical dimension
• Verma modules over p-adic Arens-Michael envelopes of reductive Lie algebras