On Moy-Prasad quotients over Laurent series fields

TL;DR

This paper introduces a stratification of Moy-Prasad quotients for reductive groups over Laurent series fields, linking conjugacy classes of twisted Levi subgroups to these quotients, aiding progress in the local geometric Langlands program.

Contribution

It defines and computes a stratification of Moy-Prasad quotients using twisted Levi subgroups, providing a new structural understanding crucial for further research.

Findings

Stratification of Moy-Prasad quotients by conjugacy classes of twisted Levi subgroups

Explicit calculation of strata in terms of twisted Levi subgroups

Foundation for future work in the local geometric Langlands program

Abstract

Let $k$ be an algebraically closed field and $G$ a connected reductive group over $k((t))$ satisfying some conditions. We define a stratification by conjugacy classes of twisted Levi subgroups of $G$ on each Moy-Prasad quotient $\mathfrak{k}_{x,r}/\mathfrak{k}_{x,r+}$ of $G$. We then calculate the strata in terms of the associated twisted Levi subgroups. This calculation is necessary for several followup papers on the local geometric Langlands program.