The Nullcone of the Lie algebra of $G_2$

Wim H. Hesselink*

*Corresponding author for this work

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This paper investigates the nilpotent conjugacy classes of the Lie algebra of the simple algebraic group of type G(2). These classes are determined by first finding the stratification, and then finding the classes within the strata. Except for characteristic 3, the classes coincide with the strata. In characteristic 3, one stratum splits into two orbits. If the characteristic differs from 2 and 3, the classes are determined by the singularities of the nilpotent variety. In characteristic 3, the matter is undecided yet. In characteristic 2, different classes have the same singularities. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)623-648
Number of pages26
JournalIndagationes mathematicae-New series
Issue number4
Publication statusPublished - Jul-2019



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