Mathematical Research Letters

Volume 10 (2003)

Number 3

A characterization of Dynkin elements

Pages: 363 – 373



Paul E. Gunnells

Eric Sommers


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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