Equivariant Vector Bundles on the Drinfeld Upper Half Space

The Drinfeld upper half space over a non-archimedean local field K is an analogue of symmetric spaces and as such has highly interesting cohomology. One aspect here are so called non-archimedean holomorphic discrete series representations of $GL_d(K)$. These arise as the global sections of homogeneous vector bundles on the projective space restricted to the Drinfeld upper half space and can be studied in the framework of locally analytic representations. We describe their structure via a generalisation of the modified parabolic induction functors $F^G_P$ due to Orlik and Strauch. This generalises work of Orlik (and in turn of Schneider-Teitelbaum and Pohlkamp) to the effect that it becomes applicable to local fields of positive characteristic as well.