Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces

For a finite extension F of Qₚ and n 1, let D be the division algebra over F of invariant 1/n and let G⁰ be the subgroup of GLₙ (F) of elements with norm 1 determinant. We show that the action of D^ on the Drinfeld tower induces an equivalence of categories from finite dimensional smooth representations of D^ to G⁰-finite GLₙ (F) -equivariant vector bundles with connection on, the (n-1) -dimensional Drinfeld symmetric space.