2009/03/02 by Dmitri I. Panyushev, Panyushev, Dmitri I. · 2 citations
Mathematics · #17B20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B20
paper · pdf · doi:10.48550/arxiv.0903.0398
6 pages, to appear in "Advances in Math"
arxiv created 2009/03/02 · openalex publication_date 2009/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let g be a simple Lie algebra over an algebraically closed field of characteristic zero. The goal of this note is to prove a closed formula for the Dynkin index of a principal sl2-subalgebra of g. The key step in the proof uses the "strange formula" of Freudenthal--de Vries. As an application, we (1) compute the Dynkin index any simple g-module regarded as sl2-module and (2) obtain an identity connecting the exponents of g and the dual Coxeter numbers of both g and the Langlands dual g^\vee.