The Dynkin index and sl(2)-subalgebras of simple Lie algebras

2013/11/13 by Dmitri I. Panyushev, Panyushev, Dmitri I. · 1 citation
Mathematics · #17B10 #17B20 #17B22 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B10 #msc:17B20 #msc:17B22

paper · pdf · doi:10.48550/arxiv.1311.3170

arxiv created 2013/11/13 · openalex publication_date 2013/11/13 · arxiv updated 2013/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a continuation of arXiv:0903.0398 [math.RT]. Let g be a simple Lie algebra. In this note, we provide simple formulae for the index of sl(2)-subalgebras in the classical Lie algebras and a new formula for the index of the principal sl(2). We also compute the difference, D, of the indices of principal and subregular sl(2)-subalgebras. Our formula for D involves some data related to the McKay correspondence for g. Using the index of sl(2)-subalgebras of classical Lie algebras, we also obtain three series of interesting combinatorial identities parameterised by partitions.

Citations

• On the Dynkin index of a principal \mathfraksl₂-subalgebra

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