Transformation Groups

, Volume 17, Issue 4, pp 1123–1190

Gradings of positive rank on simple Lie algebras

  • Mark Reeder
  • Paul Levy
  • Jiu-Kang Yu
  • Benedict H. Gross

DOI: 10.1007/s00031-012-9196-3

Cite this article as:
Reeder, M., Levy, P., Yu, JK. et al. Transformation Groups (2012) 17: 1123. doi:10.1007/s00031-012-9196-3


We complete the classification of positive rank gradings on Lie algebras of simple algebraic groups over an algebraically closed field k whose characteristic is zero or not too small, and we determine the little Weyl groups in each case. We also classify the stable gradings and prove Popov’s conjecture on the existence of a Kostant section.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Mark Reeder
    • 1
  • Paul Levy
    • 2
  • Jiu-Kang Yu
    • 3
  • Benedict H. Gross
    • 4
  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA
  2. 2.Department of Mathematics and StatisticsLancaster UniversityLancasterUK
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA
  4. 4.Department of MathematicsHarvard UniversityCambridgeUSA