Let G be a reductive group, and P a parabolic subgroup. Let L ⊆ K be finiteextensions of Qp and let G = G(L), P = P(L). In this thesis, we define the Iwasawa algebra K[[G]] and prove that it is isomorphic to the convolution algebra of compactly supported distributions on G. We show that under Schneider-Teitelbaum duality the func- tor of parabolic induction on the side of the admissible representations corresponds to the functor K[[G]] ⊗K[[P ]] − on the side of the K[[G]]-modules.This has important applications in the theory of admissible representations of G on p-adicBanach spaces. In particular, we prove the parabolic induction of an admissible represen- tation is again admissible, and prove Frobenius reciprocity for admissible representations.
| Identifer | oai:union.ndltd.org:siu.edu/oai:opensiuc.lib.siu.edu:dissertations-3224 |
| Date | 01 May 2024 |
| Creators | Roberts, Jeremiah |
| Publisher | OpenSIUC |
| Source Sets | Southern Illinois University Carbondale |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations |
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