A characterization of Dynkin elements

@article{Gunnells2002ACO,
  title={A characterization of Dynkin elements},
  author={Paul E. Gunnells and Eric N. Sommers},
  journal={Mathematical Research Letters},
  year={2002},
  volume={10},
  pages={363-373}
}
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 itsN -region. In typeAn 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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