Abelian ideals in a Borel subalgebra of a complex simple Lie algebra

2002/10/30 by Ruedi Suter · 5 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.CO #math.RT #msc:17B20 #msc:20F55

paper · pdf · doi:10.1007/s00222-003-0337-0

published as Inventiones mathematicae 156 (2004), 175-221 · 43 pages, LaTeX2e, youngtab.sty

arxiv created 2002/10/30 · openalex publication_date 2004/03/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We shall describe the abelian ideals of b in a uniform way, that is, independent of the classification of complex simple Lie algebras.

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• Abelian ideals of maximal dimension for solvable Lie algebras
• Abelian Ideals and Cohomology of Symplectic Type
• Abelian Ideals and the Variety of Lagrangian Subalgebras
• Cyclic Symmetry of the Scaled Simplex
• Maximal eigenvalues of a Casimir operator and multiplicity-free modules

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