2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73000Let $k$ 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 $\gg$.38 pages published versionGroup TheoryRings and Algebras20G25 (primary) 17B45, 20G15, 22E50 (secondary)text