From conjugacy classes in the Weyl group to unipotent classes, II
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Lusztig_From Conjugacy.pdf
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282.16 KB
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Author(s)
Lusztig, George
Date Issued
April 2012
Journal
Representation Theory
Publisher
American Mathematical Society
Citation
Lusztig, G. “From Conjugacy Classes in the Weyl Group to Unipotent Classes, II.” Representation Theory of the American Mathematical Society 16.6 (2012): 189–211. Web.© 2012 American Mathematical Society.
Version
Final published version
Abstract
Let G be a connected reductive group over an algebraically closed field of characteristic p. In an earlier paper we defined a surjective map Phi[subscript p] from the set [underline W] of conjugacy classes in the Weyl group W to the set of unipotent classes in G. Here we prove three results for Phi[subscript p]. First we show that Phi[subscript p] has a canonical one-sided inverse. Next we show that Phi[subscript 0]=r Phi[subscript p for a unique map r. Finally, we construct a natural surjective map from [underline W] to the set of special representations of W which is the composition of Phi[subscript 0] with another natural map and we show that this map depends only on the Coxeter group structure of W.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1090/S1088-4165-2012-00411-3
