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 )

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.

THERE GOES THE ELECTORAL NEIGHBORHOOD: LOCAL NETWORKS, ATTRIBUTION OF RESPONSIBILITY, AND THE (UN) FAIRNESS OF ELECTIONS

During the last two decades there have been but a handful of recorded cases of electoral fraud in Latin America. However, survey research consistently shows that often citizens do not trust the integrity of the electoral process. This dissertation addresses the puzzle by explaining the mismatch between how elections are conducted and how the process is perceived. My theoretical contribution provides a double-folded argument. First, voters’ trust in their community members (“the local experience”) impacts their level of confidence in the electoral process. Since voters often find their peers working at polling stations, negative opinions about them translate into negative opinions about the election. Second, perceptions of unfairness of the system (“the global effect”) negatively impact the way people perceive the transparency of the electoral process. When the political system fails to account for social injustice, citizens lose faith in the mechanism designed to elect representatives -and ultimately a set of policies. The fact that certain groups are systematically disregarded by the system triggers the notion that the electoral process is flawed. This is motivated by either egotropic or sociotropic considerations. To test these hypotheses, I employ a survey conducted in Costa Rica, El Salvador, Honduras, and Guatemala during May/June 2014, which includes a population-based experiment. I show that Voters who trust their peers consistently have higher confidence in the electoral process. Whereas respondents who were primed about social unfairness (treatment) expressed less confidence in the quality of the election. Finally, I find that the local experience is predominant over the global effect. The treatment has a statistically significant effect only for respondents who trust their community. Attribution of responsibility for voters who are skeptics of their peers is clear and simple, leaving no room for a more diffuse mechanism, the unfairness of the political system. Finally, now I extend analysis to the Latin America region. Using data from LAPOP that comprises four waves of surveys in 22 countries, I confirm the influence of the “local experience” and the “global effect” as determinants of the level of confidence in the electoral process.