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.

Humankindness: Illness, Animality, and the Limits of the Human in the Victorian Novel

This project posits a link between representations of animals or animality and representations of illness in the Victorian novel, and examines the narrative uses and ideological consequences of such representations. Figurations of animality and illness in Victorian fiction have been examined extensively as distinct phenomena, but examining their connection allows for a more complex view of the role of sympathy in the Victorian novel. The commonplace in novel criticism is that Victorian authors, whether effectively or not, constructed their novels with a view to the expansion of sympathy. This dissertation intervenes in the discussion of the Victorian novel as a vehicle for sympathy by positing that texts and scenes in which representations of illness and animality are conjoined reveal where the novel draws the boundaries of the human, and the often surprising limits it sets on sympathetic feeling. In such moments, textual cues train or direct readerly sympathies in ways that suggest a particular definition of the human, but that direction of sympathy is not always towards an enlarged sympathy, or an enlarged definition of the human. There is an equally (and increasingly) powerful antipathetic impulse in many of these texts, which estranges readerly sympathy from putatively deviant, degenerate, or dangerous groups. These two opposing impulses—the sympathetic and the antipathetic—often coexist in the same novel or even the same scene, creating an ideological and affective friction, and both draw on the same tropes of illness and animality. Examining the intersection of these different discourses—sympathy, illness, and animality-- in these novels reveals the way that major Victorian debates about human nature, evolution and degeneration, and moral responsibility shaped the novels of the era as vehicles for both antipathy and sympathy. Focusing on the novels of the Brontës and Thomas Hardy, this dissertation examines in depth the interconnected ways that representations of animals and animality and representations of illness function in the Victorian novel, as they allow authors to explore or redefine the boundary between the human and the non-human, the boundary between sympathy and antipathy, and the limits of sympathy itself.

Regular homomorphisms of minimal sets

The classification of minimal sets is a central theme in abstract topological dynamics. Recently this work has been strengthened and extended by consideration of homomorphisms. Background material is presented in Chapter I. Given a flow on a compact Hausdorff space, the action extends naturally to the space of closed subsets, taken with the Hausdorff topology. These hyperspaces are discussed and used to give a new characterization of almost periodic homomorphisms. Regular minimal sets may be described as minimal subsets of enveloping semigroups. Regular homomorphisms are defined in Chapter II by extending this notion to homomorphisms with minimal range. Several characterizations are obtained. In Chapter III, some additional results on homomorphisms are obtained by relativizing enveloping semigroup notions. In Veech's paper on point distal flows, hyperspaces are used to associate an almost one-to-one homomorphism with a given homomorphism of metric minimal sets. In Chapter IV, a non-metric generalization of this construction is studied in detail using the new notion of a highly proximal homomorphism. An abstract characterization is obtained, involving only the abstract properties of homomorphisms. A strengthened version of the Veech Structure Theorem for point distal flows is proved. In Chapter V, the work in the earlier chapters is applied to the study of homomorphisms for which the almost periodic elements of the associated hyperspace are all finite. In the metric case, this is equivalent to having at least one fiber finite. Strong results are obtained by first assuming regularity, and then assuming that the relative proximal relation is closed as well.