Computing with nilpotent orbits in simple Lie algebras of exceptional type
Willem A. de Graaf
Abstract: Let G be a simple algebraic group over an algebraically
closed field with Lie algebra g. Then the orbits of nilpotent
elements of g under the adjoint action of G have been
classified. We describe a simple algorithm for finding a
representative of a nilpotent orbit. We use this to compute lists of
representatives of these orbits for the Lie algebras of exceptional
type. Then we give two applications. The first one concerns settling
a conjecture by Elashvili on the index of centralizers of nilpotent
orbits, for the case where the Lie algebra is of exceptional type.
The second deals with minimal dimensions of centralizers in
centralizers.
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