Equivariant vector bundles with connection on the p-adic half-plane

Recent joint work with Konstantin Ardakov has been devoted to classifying equivariant line bundles with flat connection on the Drinfeld p-adic half-plane defined over F, a finite extension of Q_p, and proving that their global sections yield admissible locally analytic representations of GL_2(F) of finite length. In this talk we will discuss this work and invite reflection on how it might be extended to equivariant vector bundles with connection on the p-adic half-plane and, if time permits, to higher dimensional analogues of the half-plane.