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Local systems on nilpotent orbits and weighted Dynkin diagrams
Author(s):
Pramod
N.
Achar;
Eric
N.
Sommers
Journal:
Represent. Theory
6
(2002),
190-201.
MSC (2000):
Primary 17B10, 32L20
Posted:
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.
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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:
10.1090/S1088-4165-02-00174-7
PII:
S 1088-4165(02)00174-7
Received by editor(s):
December 14, 2001
Received by editor(s) in revised form:
July 26, 2002
Posted:
September 5, 2002
Copyright of article:
Copyright
2002,
American Mathematical Society
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