A characterization of Dynkin elements

PE Gunnells, University of Massachusetts - Amherst
E Sommers, University of Massachusetts - Amherst

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This is the pre-published version harvested from ArXiv. The published version is located at

http://www.mathjournals.org/mrl/2003-010-003/2003-010-003-006.pdf

http://www.mathjournals.org/mrl/2003-010-003/index.html

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, which leads to some conjectures in representation theory.