On some properties of the functors ${\mathcal F}^G_P$ from Lie algebra to locally analytic representations

Sascha Orlik, Matthias Strauch

Published 2018-02-21Version 1

For a split reductive group $G$ over a finite extension $L$ of ${\mathbb Q}_p$, and a parabolic subgroup $P \subset G$ we examine functorial properties of the functors ${\mathcal F}^G_P$ introduced in \cite{OS2,OS3}. We discuss the aspects of faithfulness, projective and injective objects, Ext-groups and some kind of adjunction formulas. Here we apply the (naive) Jacquet functor and a more detailed study of the category ${\mathcal O}^B$ introduced in \cite{OS3}.