In Part I, we investigate the principal series representations of the n-fold covering groups of the special linear group over a p-adic field. Such representations are constructed via the Stone-von Neumann theorem. We have three interrelated results. We first compute the K-types of these representations. We then give a complete set of reducibility points for the unramified principal series representations. Among these are the unitary unramified principal series representations, for which we further investigate the distribution of the K-types among its irreducible components.
In Part II, we demonstrate another application of the Stone-von Neumann theorem. Namely, we present a lower bound for the minimal degree of a faithful representation of an adjoint Chevalley group over a quotient ring of a non-Archimedean local field.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/34240 |
| Date | January 2016 |
| Creators | Karimianpour, Camelia |
| Contributors | Nevins, Monica, Salmasian, Hadi |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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