On 𝔰𝔩2-triples for classical algebraic groups in positive characteristic

Simon M. Goodwin, Rachel Pengelly

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Abstract

Let 𝕜 be an algebraically closed field of characteristic p > 2, let n ∈ ℤ>0, and take G to be one of the classical algebraic groups GLn(𝕜), SLn(𝕜), Spn(𝕜), On(𝕜) or SOn(𝕜), with 𝔤 = Lie G. We determine the maximal G-stable closed subvariety V of the nilpotent cone N of 𝔤 such that the G-orbits in V are in bijection with the G-orbits of 𝔰𝔩2-triples (e, h, f) with e, f ∈ V. This result determines to what extent the theorems of Jacobson–Morozov and Kostant on 𝔰𝔩2-triples hold for classical algebraic groups over an algebraically closed field of “small” odd characteristic. 
Original languageEnglish
JournalTransformation Groups
DOIs
Publication statusPublished - 20 May 2022

Bibliographical note

Funding Information:
The results in this paper form part of the PhD research of the second author, who received financial support from the EPSRC grant EP/R513167/1. The first author is supported by EPSRC grant EP/R018952/1.

Publisher Copyright:
© 2022, The Author(s).

Keywords

  • Algebraic groups
  • Lie algebras
  • Positive characteristic
  • sl -triples

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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