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

Abstract

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 ${\mathcal{F}}_P^G$ introduced in \cite{OS2}. We discuss the aspects of faithfulness, projective and injective objects, Ext-groups and some kind of adjunction formulas.

arXiv commentIn this revised version we have removed many mistakes which appeared in the first version. In particular section 3 has been withdrawn

References in corpus (1)

• The Jordan-Hölder series of the locally analytic Steinberg representation