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Equivariant line bundles with connection on the Drinfeld upper half-space Ω⁽²⁾ https://doi.org/10.17863/CAM.106950 Zhu, Yiyue Wadsley, Simon Ardakov and Wadsley developed a theory of $\mathscr{D}$-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. University of Cambridge 2023-05-01 Thesis Doctoral Doctor of Philosophy (PhD) eng Cambridge Trust Corpus Christi College Department of Pure Mathematics and Mathematical Statistics https://www.repository.cam.ac.uk/handle/1810/365880 controlled.access https://www.repository.cam.ac.uk/bitstreams/aa77b0cf-8188-4c9b-a075-9b742fa3040e/download 0f6da30c2fa7364e39fcc755116230a3 https://www.repository.cam.ac.uk/bitstreams/1a098187-5c5e-451a-b215-5cd2c3fa5fa5/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ Drinfeld half-space locally analytic representation p-adic