Ardakov and Wadsley developed a theory of $D$-modules on rigid analytic spaces and established a Beilinson-Bernstein style localisation theorem for coadmissible modules over the locally analytic distribution algebra. Using this theory, they obtained admissible locally analytic representations of GL₂ by studying equivariant line bundles with connection on the Drinfeld half-plane Ω⁽¹⁾. In this thesis, we will follow the idea of Ardakov-Wadsley and extend their techniques to GL₃ by studying the Drinfeld upper half-space Ω⁽²⁾ of dimension 2.