A note on exponents vs root heights for complex simple Lie algebras

2006/09/08 by Sankaran Viswanath, Viswanath, Sankaran
Mathematics · #05E15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E15

paper · pdf · doi:10.48550/arxiv.math/0609248

5 pages

arxiv created 2006/09/08 · openalex publication_date 2006/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an elementary combinatorial proof of a special case of a result due to Bazlov and Ion concerning the Fourier coefficients of the Cherednik kernel. This can be used to give yet another proof of the classical fact that for a complex simple Lie algebra, the partition formed by its exponents is dual to that formed by the numbers of positive roots at each height.

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