RIGID ORBITS AND SHEETS IN REDUCTIVE LIE ALGEBRAS 1 OVER FIELDS OF PRIME CHARACTERISTIC

Research output: Contribution to journalArticle

  • Authors:
  • Alexander Premet
  • David I. Stewart

Abstract

Let be a simple simply connected algebraic group over an algebraically closed field of characteristic with . We discuss various properties of nilpotent orbits in , which have previously only been considered over . Using computational methods, we extend to positive characteristic various calculations of de Graaf with nilpotent orbits in exceptional Lie algebras. In particular, we classify those orbits which are reachable as well as those which satisfy a certain related condition due to Panyushev, and determine the codimension of the derived subalgebra in the centraliser of any nilpotent element . Some of these calculations are used to show that the list of rigid nilpotent orbits in , the classification of sheets of and the distribution of the nilpotent orbits amongst them are independent of good characteristic, remaining the same as in the characteristic zero case. We also give a comprehensive account of the theory of sheets in reductive Lie algebras over algebraically closed fields of good characteristi

Bibliographical metadata

Original languageEnglish
JournalJournal of the Institute of Mathematics of Jussieu
Early online date4 Apr 2016
DOIs
StateE-pub ahead of print - 4 Apr 2016