Local Systems on Nilpotent Orbits and Weighted Dynkin Diagrams

Details Local Systems on Nilpotent Orbits and Weighted Dynkin Diagrams Local Systems on Nilpotent Orbits and Weighted Dynkin Diagrams

2002-01-25

arxiv.org/abs/math/0201248v1

Mathematics

Representation Theory

11 pages

Scientific paper

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.

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