Local systems on nilpotent orbits and weighted Dynkin diagrams
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- by Pramod N. Achar and Eric N. Sommers
- Represent. Theory 6 (2002), 190-201
- DOI: https://doi.org/10.1090/S1088-4165-02-00174-7
- Published electronically: September 5, 2002
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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.References
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Bibliographic Information
- Pramod N. Achar
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 701892
- Email: pramod@math.uchicago.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Represent. Theory 6 (2002), 190-201
- MSC (2000): Primary 17B10, 32L20
- DOI: https://doi.org/10.1090/S1088-4165-02-00174-7
- MathSciNet review: 1927953