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Journal of Lie Theory 19 (2009), No. 2, 371--390
Copyright Heldermann Verlag 2009

On Exceptional Nilpotents in Semisimple Lie Algebras

Alexander G. Elashvili
Razmadze Mathematical Institute, M. Alexidze St. 1, Tbilisi 0193, Georgia

Victor G. Kac
Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, U.S.A.

Ernest B. Vinberg
Moscow State University, Department of Mathematics, Moscow 119992, GSP-2, Russia

We classify all pairs (m,e), where m is a positive integer and e is a nilpotent element of a simple Lie algebra, that arise in connection with the classification of simple rational W-algebras.

Keywords: Simple Lie algebra, nilpotent orbit, centralizer, Coxeter number, Levi subalgebra.

MSC: 17B20; 17B69

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