A characterization of Dynkin elements

2002/12/05 by Paul E. Gunnells, Eric Sommers, Gunnells, Paul E. +1
Mathematics · #17B10 #17B35 #20F55 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:17B10 #msc:17B35 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0212089

9 pages

openalex publication_date 2002/12/05 · arxiv created 2003/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a Dynkin element is the unique point of minimal length in its N-region. In type A_n this translates into a statement about the regions determined by the canonical left Kazhdan-Lusztig cells. Some possible generalizations are explored in the last section.

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