The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )
| dc.contributor.advisor | Adams, Jeffrey D | en_US |
| dc.contributor.author | Cui, Ran | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2016-06-22T06:03:27Z | |
| dc.date.available | 2016-06-22T06:03:27Z | |
| dc.date.issued | 2016 | en_US |
| dc.description.abstract | The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence. | en_US |
| dc.identifier | https://doi.org/10.13016/M2KJ5B | |
| dc.identifier.uri | http://hdl.handle.net/1903/18318 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | c-Invariant Hermitian Form | en_US |
| dc.subject.pquncontrolled | Extended Group | en_US |
| dc.subject.pquncontrolled | Frobenius-Schur Indicator | en_US |
| dc.subject.pquncontrolled | Langlands Correspondence | en_US |
| dc.subject.pquncontrolled | Real-Quaternionic Indicator | en_US |
| dc.title | The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F ) | en_US |
| dc.type | Dissertation | en_US |
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