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Faithfulness of highest-weight modules for Iwasawa algebras https://doi.org/10.17863/CAM.99798 Mann, Stephen Wadsley, Simon James We prove faithfulness of infinite-dimensional generalised Verma modules for Iwasawa algebras corresponding to split simple Lie algebras with a Chevalley basis. We use this to prove faithfulness of all infinite-dimensional highest-weight modules in the case of type *A*. In this case we also show that all non-zero two-sided ideals of the corresponding Iwasawa algebras have finite codimension, and in particular all non-zero prime ideals are annihilators of finite-dimensional simple modules. University of Cambridge 2022-09-30 Thesis Doctoral Doctor of Philosophy (PhD) eng EPSRC grant. https://www.repository.cam.ac.uk/handle/1810/353740 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/aa109156-177b-4a6e-a5df-2b89de05713a/download 5dfe69772c01b9c4493bb296d396d3bc https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/2b1f1192-2d0b-4be2-9da1-27575202794b/download 87eda9de84448d1f82354d60eee3eb5f https://creativecommons.org/licenses/by/4.0/ Noncommutative Algebra Representation Theory