Local systems on nilpotent orbits and weighted Dynkin diagrams
This is the pre-published version harvested from ArXiv. The published version is located at http://www.ams.org/journals/ert/2002-006-07/S1088-4165-02-00174-7/
We study the Lusztig-Vogan bijection for the case of a local system. We compute the bijection explicitly in type A for a local system and then show that the dominant weights obtained for different local systems on the same orbit are related in a manner made precise in the paper. We also give a conjecture (putatively valid for all groups) detailing how the weighted Dynkin diagram for a nilpotent orbit in the dual Lie algebra should arise under the bijection.
Promad Achar and E Sommers. "Local systems on nilpotent orbits and weighted Dynkin diagrams" Representation Theory 6 (2002): 190-201.
Available at: http://works.bepress.com/eric_sommers/2