On ๐”ฐ๐”ฉ2-triples for classical algebraic groups in positive characteristic

Simon M. Goodwin, Rachel Pengelly

Research output: Contribution to journal โ€บ Article โ€บ peer-review

Abstract

Let ๐•œ be an algebraically closed field of characteristic p > 2, let n โˆˆ โ„ค>0, and take G to be one of the classical algebraic groups GLn(๐•œ), SLn(๐•œ), Spn(๐•œ), On(๐•œ) or SOn(๐•œ), with ๐”ค = Lie G. We determine the maximal G-stable closed subvariety V of the nilpotent cone N of ๐”ค such that the G-orbits in V are in bijection with the G-orbits of ๐”ฐ๐”ฉ2-triples (e, h, f) with e, f โˆˆ V. This result determines to what extent the theorems of Jacobsonโ€“Morozov and Kostant on ๐”ฐ๐”ฉ2-triples hold for classical algebraic groups over an algebraically closed field of โ€œsmallโ€ odd characteristic.ย 
Original languageEnglish
JournalTransformation Groups
Publication statusAccepted/In press - 31 Jan 2021

Bibliographical note

Not yet published as of 09/05/2022.

Keywords

  • Lie algebras
  • sl2 triples

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