Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

Let $G$ be a complex reductive group. A fundamental stratum for $G$ is a triple $(x,r,\beta)$ where $x$ is a point in the Bruhat-Tits building of $G$, $r$ is a nonnegative real number called depth of the stratum, and $\beta$ is a semistable functional on the Moy-Prasad filtration of $\fg$ associated to $x$ at level $r$. Fundamental strata were first introduced to classify admissible representations of a $p$-adic reductive group. More recently, Bremer and Sage have shown that fundamental strata play an important role in the geometric Langlands program and developed a theory of fundamental strata for $G$-connections. In this dissertation, we generalize Bremer and Sage's result and develop a theory of fundamental strata for twisted $G$-connection. We show that every twisted $G$-connection contains a fundamental stratum, and every fundamental stratum contained in a twisted $G$-connection has the same depth, which we now called the slope. We also give characterizations and properties of slope. Lastly, we construct examples of a twisted formal Frenkel-Gross connection for classical groups.

Date

7-10-2025

Committee Chair

Achar, Pramod N

DOI

10.31390/gradschool_dissertations.6851

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