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A classification of the principal nilpotent pairs in simple Lie algebras and related problems

1999/09/15 by Alexander G. Elashvili, A. G. Élashvili, Elashvili, Alexander G. +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/9909082

22 pages, LaTeX 2.09

arxiv created 1999/09/15 · openalex publication_date 1999/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a classification of the principal and distinguished nilpotent pairs in all classical Lie algebras. As a classification of the principal pairs in the exceptional simple Lie algebras was obtained earlier (see Appendix to Ginzburg's preprint math.AG/9903059), we thus have a complete classification of principal nilpotent pairs.

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