Equivariant vector bundles on Drinfeld's upper half space

摘要

Let X subset of P-K(d) be Drinfeld's upper half space over a finite extension K of Q(p). We construct for every GL(d+1)-equivariant vector bundle F on P-K(d), a GL(d+1)(K)-equivariant filtration by closed subspaces on the K-Frechet H-0( X, F). This gives rise by duality to a filtration by locally analytic GL(d+1)(K)-representations on the strong dual H-0(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].