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Parametrizing nilpotent orbits via Bruhat-Tits theory

Stephen DeBacker
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Abstract

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 $\gg$ denote the Lie algebra of $G$. Fix $r \in \R$. 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 $\gg$.

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Stephen DeBacker. 2004-10-25. Parametrizing nilpotent orbits via Bruhat-Tits theory. https://arxiv.org/abs/math/0410533

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