Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
In 2013, Reeder and Yu introduced certain low positive depth supercuspidal representations of $p$-adic groups called \textit{epipelagic} representations. These representations generalize the simple supercuspidal representations of Gross and Reeder, which have the lowest possible depth. Epipelagic representations also arise in recent work on the Langlands correspondence; for example, simple supercuspidals appear in the automorphic data corresponding to the Kloosterman $l$-adic sheaf. In this thesis, we take a first step towards the construction of ``\textit{mesopelagic} representation (of Iwahori type)'' which are the higher depth analogues of simple supercuspidal representations. We see that these constructions can be done in a similar way as the epipelagics of Reeder-Yu.
Date
7-22-2024
Recommended Citation
Agarwal, Prerna, "Diving Deeper into Supercuspidal Representations" (2024). LSU Doctoral Dissertations. 6549.
https://repository.lsu.edu/gradschool_dissertations/6549
Committee Chair
Achar, Pramod N.