Analytic vectors in continuous p-adic representations
Representation Theory
2014-01-14 v2 Number Theory
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.
Cite
@article{arxiv.0711.2008,
title = {Analytic vectors in continuous p-adic representations},
author = {Tobias Schmidt},
journal= {arXiv preprint arXiv:0711.2008},
year = {2014}
}
Comments
Final version (appeared in Comp. Math. 2009). Exposition shortened. Minor items corrected