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

DOI:
https://doi.org/10.1090/S1088-4165-02-00174-7

Published electronically:
September 5, 2002

MathSciNet review:
1927953

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Abstract | References | Similar Articles | Additional Information

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

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

DOI:
https://doi.org/10.1090/S1088-4165-02-00174-7

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