Equivariant vector bundles on Drinfeld's upper half space [article]

Sascha Orlik
2007 arXiv   pre-print
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.
more » ... This paper generalizes the cases of the canonical bundle due to Schneider and Teitelbaum and that of the structure sheaf by Pohlkamp.
arXiv:math/0606355v3 fatcat:i2y2vvekeveyxersggv6mb7afq