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

Let G be a simple algebraic group over k = C, or F-p where p is good. Set g = Lie G. Given r is an element of N and a faithful (restricted) representation rho: g --> gl(V), one can define a variety of nilpotent elements N-r,(rho)(g) = {x is an element of g: rho(x)(r) = 0}. In this paper we determine this variety when rho is an irreducible representation of minimal dimension or the adjoint representation. (C) 2004 Elsevier Inc. All rights reserved.