Equivariant vector bundles on Drinfeld's upper half space
Abstract
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 KFrechet 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606355
 Bibcode:
 2006math......6355O
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Representation Theory;
 11F70;
 11F85;
 22E50
 EPrint:
 72 pages, error in Prop. 1.4.2 has been fixed, changed slightly the content