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# A Classification of the Principal Nilpotent Pairs in Simple Lie Algebras and Related Problems

@inproceedings{Elashvili2001ACO, title={A Classification of the Principal Nilpotent Pairs in Simple Lie Algebras and Related Problems}, author={Alexander Grigorievich Elashvili and Dmitri I. Panyushev}, year={2001} }

- Published 2001
DOI:10.1017/S0024610700001903

Let g be a semisimple Lie algebra over an algebraically closed field k of characteristic zero and G its adjoint group. The notion of a principal nilpotent pair is a double counterpart of the notion of a regular (= principal) nilpotent element in g. Roughly speaking, a principal nilpotent pair e = (e1, e2) consists of two commuting elements in g that can independently be contracted to the origin and such that their simultaneous centralizer has the minimal possible dimension, i.e., rk g. The very… CONTINUE READING