Equivariant Vector Bundles on Drinfeld’s Upper Half Space

Let X ⊂ PK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H0(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H0(X ,F)′. The graded pieces of this filtration are locally analytic induced representations from locally algebraic ones with respect to maximal parabolic subgroups. This paper generalizes the cases of the canonical bundle due to Schneider and Teitelbaum [ST1] and that of the structure sheaf by Pohlkamp [P].