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Computing with Nilpotent Orbits in Simple Lie Algebras of Exceptional Type

Published online by Cambridge University Press:  01 February 2010

Willem A. de Graaf
Willem A. de Graaf
Affiliation:
Dipartimento di Matematica, Università di Trento, via Sommarive 14, I-38100 Povo (Trento), Italy, degraaf@science.unitn.it

Abstract

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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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 11 , 2008 , pp. 280 - 297
Copyright
Copyright © London Mathematical Society 2008

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Supplementary material: File

JCM 11 Graaf Appendix A

Graaf Appendix A

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