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Gradings of positive rank on simple Lie algebras

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Boston College, Chestnut Hill, MA, 02467, USA

    Mark Reeder

  2. Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK

    Paul Levy

  3. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jiu-Kang Yu

  4. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Benedict H. Gross

Authors
  1. Mark Reeder
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  2. Paul Levy
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  3. Jiu-Kang Yu
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  4. Benedict H. Gross
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Correspondence to Mark Reeder.

Additional information

Supported by NSF grants DMS-0801177 and DMS-0854909. (Mark Reeder)

Supported by NSF grant DMS-0854909. (Jiu-Kang Yu)

Supported by NSF grant DMS-0901102. (Benedict H. Gross)

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Reeder, M., Levy, P., Yu, JK. et al. Gradings of positive rank on simple Lie algebras. Transformation Groups 17, 1123–1190 (2012). https://doi.org/10.1007/s00031-012-9196-3

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