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.Comment: 9 page

Gunnells, Paul E.

Sommers, Eric

English

arXiv

Paul E. Gunnells

Eric Sommers

Crossref

Mathematical Research Letters

A characterization of Dynkin elements

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

Gunnells, PE

Sommers, E

ScholarWorks@UMass Amherst

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.htmlWe 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.363-37

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.238.1395

A characterization of Dynkin elements

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