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We describe the locally analytic $\mathrm{GL}_d(K)$-representations whicharise as the global sections of homogeneous vector bundles on the projectivespace restricted to the Drinfeld upper half space over a non-archimedean localfield $K$. We thereby generalize work of Orlik (2008) for $p$-adic fields tothe effect that it becomes applicable to local fields of positivecharacteristic. Our description of this space of global sections is in terms ofa filtration by subrepresentations, and a characterization of the resultingsubquotients via adaptations of the functors $\mathcal{F}^G_P$ considered byOrlik-Strauch (2015) and Agrawal-Strauch (2022). For a local field $K$ ofpositive characteristic, we also determine the locally analytic (resp.continuous) characters of $K^\times$ with values in $K$-Banach algebras whichare integral domains (resp. with values in finite extensions of $K$) in anappendix.

Equivariant Vector Bundles on the Drinfeld Upper Half Space over a Local Field of Positive Characteristic