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}
}
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

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SHOWING 1-2 OF 2 REFERENCES

Nilpotent orbits in semisimple Lie algebras

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Towards a classification of principal nilpotent pairs

  • A. G. Elashvili, D. Panyushev

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