The Categories of Lubin-Tate and Drinfeld Bundles

For a finite extension $F$ of ${\mathbb{Q}}_p$ and $n\ge 1$, we show that the category of Lubin-Tate bundles on the $(n-1)$-dimensional Drinfeld symmetric space is equivalent to the category of finite-dimensional smooth representations of the group of units of the division algebra of invariant $1\mathrm{/}n$ over $F$.