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Varieties of nilpotent elements for simple Lie algebras I: Good primes

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  • David J. Benson
  • Phil Bergonio
  • Brian D. Boe
  • Leonard Chastkofsky
  • Bobbe Cooper
  • G. Michael Guy
  • Jo Jang Hyun
  • Jerome Jungster
  • Graham Matthews
  • Nadia Mazza
  • Daniel K. Nakano
  • Kenyon Platt
<mark>Journal publication date</mark>15/10/2004
<mark>Journal</mark>Journal of Algebra
Issue number2
Number of pages19
Pages (from-to)719-737
Publication StatusPublished
<mark>Original language</mark>English


Let G be a simple algebraic group over k = ℂ, or F̄p where p is good. Set g = Lie G. Given r ∈ ℕ and a faithful (restricted) representation ρ: g → gl(V), one can define a variety of nilpotent elements Nr,ρ(g) = {x ∈ g: ρ(x)r = 0}. In this paper we determine this variety when ρ is an irreducible representation of minimal dimension or the adjoint representation.