Abelian ideals with given dimension in Borel subalgebras

2008/08/15 by Li Luo, Luo, Li
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.0808.2086

18 pages

arxiv created 2008/08/15 · arxiv updated 2009/12/01

Abstract

A well-known Peterson's theorem says that the number of abelian ideals in a Borel subalgebra of a rank-r finite dimensional simple Lie algebra is exactly 2^r. In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra of finite dimensional simple Lie algebras, which is a refinement of the Peterson's theorem capturing more Lie algebra invariants.

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