In this thesis, we classify up to conjugacy the maximal elliptic toral subgroups of all
special orthogonal groups SO(V), where (q,V) is a 4-dimensional quadratic space
over a non-archimedean local field of odd residual characteristic. Our parameterization blends the abstract theory of Morris with a generalization of the practical work
performed by Kim and Yu for Sp(4). Moreover, we compute an explicit Witt basis
for each such torus, thereby enabling its concrete realization as a set of matrices embedded into the group. This work can be used explicitly to construct supercuspidal
representations of SO(V).
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/42759 |
| Date | 29 September 2021 |
| Creators | Chinner, Trinity |
| Contributors | Nevins, Monica |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Attribution-NoDerivatives 4.0 International, http://creativecommons.org/licenses/by-nd/4.0/ |
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