Sheaves on the Bruhat-Tits building and p-adic representations

Let $G$ be a $p$-adic split reductive group. In this talk we describe a functor
from admissible locally analytic representations of $G$ with infinitesimal character to certain equivariant sheaves on its Bruhat-Tits building. This generalizes work of Schneider-Stuhler on smooth representations. The construction is alsocompatible with the localisation of $Lie(G)$-modules on the flag variety by Beilinson-Bernstein. This is joint work with D. Patel/M. Strauch