Parametrizing nilpotent orbits via Bruhat-Tits theory


Let $k$ denote a field with nontrivial discrete valuation. We assume that $k$ is complete with perfect residue field. Let $G$ be the group of $k$-rational points of a reductive, linear algebraic group defined over $k$. Let $\frak g$ denote the Lie algebra of $G$. Fix $r\in \mathbb{R}$. Subject to some restrictions, we show that the set of distinguished degenerate Moy-Prasad cosets of depth $r$ (up to an equivalence relation) parametrizes the nilpotent orbits in $\frak g$.


Stephen DeBacker