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Local systems on nilpotent orbits and weighted Dynkin diagrams

Authors: Pramod N. Achar and Eric N. Sommers
Journal: Represent. Theory 6 (2002), 190-201
MSC (2000): Primary 17B10, 32L20
Published electronically: September 5, 2002
MathSciNet review: 1927953
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Abstract: 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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Additional Information

Pramod N. Achar
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Eric N. Sommers
Affiliation: Department of Mathematics, University of Massachusetts—Amherst, Amherst, Massachusetts 01003
Address at time of publication: School of Mathematics, IAS, Princeton, New Jersey 08540

Received by editor(s): December 14, 2001
Received by editor(s) in revised form: July 26, 2002
Published electronically: September 5, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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