Equivariant vector bundles on Drinfeld's upper half space
Abstract
Description
Let X be Drinfeld's upper half space of dimension d over a finite extension K of Q_p. We construct for every homogeneous vector bundle F on the projective space P^d a GL_{d+1}(K)-equivariant filtration by closed K-Frechet spaces on F(X). This gives rise by duality to a filtration by locally analytic GL_{d+1}(K)-representations on the strong dual. 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 and that of the structure sheaf by Pohlkamp.
72 pages, error in Prop. 1.4.2 has been fixed, changed slightly the content
72 pages, error in Prop. 1.4.2 has been fixed, changed slightly the content