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Representation Theory
Representation Theory
ISSN 1088-4165

 

A topological approach to induction theorems in Springer theory


Author: David Treumann
Journal: Represent. Theory 13 (2009), 8-18
MSC (2000): Primary 32S30
Published electronically: February 6, 2009
MathSciNet review: 2480385
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Abstract: We give a self-contained account of a construction due to Rossmann, which lifts Springer's action of a Weyl group on the cohomology of a Springer fiber to an action on its homotopy type. We use this construction to produce a generalization of an ``induction theorem'' of Alvis and Lusztig, which relates the Springer representations attached to a reductive group to those attached to a Levi subgroup. Our generalization applies to more general centralizers and to representations of Weyl groups on mod $ p$ cohomology.


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Additional Information

David Treumann
Affiliation: Department of Mathematics, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, Minnesota 55455

DOI: http://dx.doi.org/10.1090/S1088-4165-09-00342-2
PII: S 1088-4165(09)00342-2
Received by editor(s): October 14, 2008
Published electronically: February 6, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.