Covers for self-dual supercuspidal representations of the Siegel Levi subgroup of classical p-adic groups

We study components of the Bernstein category for a p-adic classical group (with p odd) with inertial support a self-dual positive level supercuspidal representation of a Siegel Levi subgroup. More precisely, we use the method of covers to construct a Bushnell-Kutzko type for such a component. A detailed knowledge of the Hecke algebra of the type should have number-theoretic implications.Comment: 22 page

Does eye examination order for standard automated perimetry matter?

PURPOSE: In spite of faster examination procedures, visual field (VF) results are potentially influenced by fatigue. We use large-scale VF data collected from clinics to test the hypothesis that perimetric fatigue effects are greater in the eye examined second. METHODS: Series of six Humphrey Swedish Interactive Testing Algorithm (SITA) VFs from 6901 patients were retrospectively extracted from a VF database from four different glaucoma clinics. Mean deviation (MD) was compared between first and second tested eyes. A surrogate measure of longitudinal MD variability over time was estimated from errors using linear regression of MD against time then compared between first and second tested eye. RESULTS: Right eye VF was tested consistently first throughout in 6320 (91.6%) patients. Median (interquartile range; IQR) MD in the first tested (right) eye and second tested (left) eye was -2.57 (-6.15, -0.58) dB and -2.70 (-6.34, -0.80) dB respectively (median reduction VF sensitivity of 0.13 dB; p < 0.001). Median (IQR) increase in our surrogate measure of longitudinal MD variability in the second eye tested was 3% (-43%, 50%); this effect was not associated with patient age or rest time between examinations. CONCLUSION: Statistically significant perimetric fatigue effects manifest on average in the second eye tested in routine clinics using Humphrey Field Analyzer SITA examinations. However, the average effects were very small and there was enormous variation among patients. We recommend starting with a right eye examination so that any perimetric fatigue effects, if they exist in an individual, will be as constant as possible from visit to visit

On Representations of General Linear Groups over Principal Ideal Local Rings of Length Two

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of all such groups which preserves dimensions. For general linear groups of order three and four over these rings, we construct all the irreducible representations. We show that the the problem of constructing all the irreducible representations of all general linear groups over these rings is not easier than the problem of constructing all the irreducible representations of the general linear groups over principal ideal local rings of arbitrary length in the function field case.Comment: 21 page

Branching Rules for Supercuspidal Representations of SL_2(k)

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this decomposition in the case that the residual characteristic is odd, and determine how the spectrum of this decomposition varies as a function of the parameters describing the supercuspidal representation.Comment: 30 pages; minor reorganization to previous version. Accepted to Journal of Algebr

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

Herodas, mime, and comedy: Tradition and reception in Mimiamboi 6 and 7.

Herodas, a third century contemporary of Theocritus and Callimachus, combined thematic and structural elements from the dramatic character sketches of the popular mimos with the language and the meter of the seventh century B.C. Ionic poet Hipponax to create a new poetic form: the Mimiamboi. This odd combination has raised the question of how Herodas intended his work to be received. Some have thought that his mimes were meant to be staged like the popular mimos, while others have contended that the mimes were recited in symposiastic settings, like the iambic poetry of Hipponax. I argue, however, that Herodas designed his mimes to evoke dramatic action on the written page. I do not focus on reception solely as a historical question, but rather as a means to understanding more clearly Herodas' importance in both the Greek and Latin literary traditions. In the first three chapters I concentrate on Mimes 6 and 7, the two poems which have caused the most scholarly dissent at the levels of both design and literary meaning. Through literary commentaries in Chapters One and Two, I draw attention to the comic and mimic influences in Herodas' poetry and address textual and performative issues as they affect the overall interpretation of the action. In the third chapter I examine the connection between Mimes Six and Seven. The mimes are clearly related, but the differences between setting and subject-matter have been a constant source of debate. I argue that Herodas creates a mystery at the end of 6 which is only solved when we read the beginning of 7. This design, like the elegiac diptychs of Propertius and Ovid, suggests a textual imitation of dramatic action. In the fourth and final chapter, I examine more specifically how Herodas engages his audience by comparing the comic eavesdropping scenarios in Mime 1, Plautus Mostellaria i.iii and Ovid Amores I.8. I end my study by placing Herodas firmly within the Hellenistic tradition which influenced the techniques of so much later Greek and Latin poetry.Ph.D.Ancient languagesClassical literatureCommunication and the ArtsLanguage, Literature and LinguisticsTheaterUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130989/2/3042211.pd