Analytic vectors in continuous p-adic representations

TL;DR

This paper develops a functorial framework connecting admissible p-adic Banach space representations with locally analytic representations for certain p-adic Lie groups, extending the concept of analytic vectors beyond Q_p.

Contribution

It constructs an exact, faithful functor from admissible G-Banach space representations to locally analytic G_0-representations, generalizing the passage to analytic vectors for arbitrary base fields.

Findings

Constructed a functor linking Banach and locally analytic representations.

Analyzed derived functors of passage to analytic vectors.

Determined higher analytic vectors in specific induced 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.