From conjugacy classes in the Weyl group to unipotent classes, II
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
American Mathematical Society
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.
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