Mathematical Research Letters

Volume 10, Issue 3, May 2003 pp. 363-373.

A characterization of Dynkin elements

Authors: Paul E. Gunnells and Eric Sommers
Author institution: University of Massachusetts

Summary: 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.

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