Local systems on nilpotent orbits and weighted dynkin diagrams
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. © 2002 American Mathematical Society.
Publication Source (Journal or Book title)
Achar, P., & Sommers, E. (2002). Local systems on nilpotent orbits and weighted dynkin diagrams. Representation Theory, 6 (7), 190-201. https://doi.org/10.1090/S1088-4165-02-00174-7