
Journal of Lie Theory 27 (2017), No. 1, 001042 Copyright Heldermann Verlag 2017 Nilpotent Orbits: Finiteness, Separability and Howe's Conjecture Julius Witte Radboud Universiteit Nijmegen, Heyendaalseweg 135, Nijmegen  6525AJ, The Netherlands J.Witte@math.ru.nl This paper is about nilpotent orbits of reductive groups over local nonArchimedean fields. We will try to identify for which groups there are only finitely many nilpotent orbits, for which groups the nilpotent orbits are separable and for which groups Howe's conjecture holds. For split reductive groups we get a classification in terms of the root data and the characteristic of the underlying local field. For this classification the proof of the failure of Howe's conjecture for split reductive groups for which the characteristic of the field is bad and the proof of Howe's conjecture for the projective linear group are the key results. For general reductive groups we get some partial results, among which there is a proof of Howe's conjecture for groups for which all nilpotent orbits are separable. Keywords: Nilpotent orbits, Howe's conjecture, reductive groups over local nonArchimedean fields. MSC: 20G25, 22E50, 17B45 [ Fulltextpdf (482 KB)] for subscribers only. 