Parametrizing nilpotent orbits via Bruhat-Tits theory

2004/10/25 by Stephen DeBacker
Mathematics · #math.GR #math.RA #msc:20G25 #msc:17B45 #msc:20G15 #msc:22E50

paper · pdf

published as Ann. of Math. (2), Vol. 156 (2002), no. 1, 295--332 · 38 pages published version

arxiv created 2004/10/25 · arxiv updated 2009/12/01

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 ≫ denote the Lie algebra of G. Fix r ∈ \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 ≫.

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