The Drinfeld upper half space is defined as the complement of all K-rational hyperplanes in the projective space over a local non-archimedean field K. It is a non-archimedean analogue of a symmetric spaces, and therefore one is interested in its cohomology. For a homogeneous vector bundle on the projective space restricted to the Drinfeld upper half space, the dual of its rigid analytic sections is a locally analytic GL_d(K)-representation. We describe the structure of representations arising this way via a filtration by subrepresentations and interpret the resulting subquotients in terms of an adaptation of the modified induction functors F^G_P due to Orlik and Strauch. This generalizes work of Orlik (in turn based on work of Schneider-Teitelbaum and Pohlkamp) for the case of p-adic K."