On Some Partitions of a Flag Manifold
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Lusztig_On some.pdf
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111.78 KB
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Author(s)
Lusztig, George
Date Issued
March 2011
Journal
Asian Journal of Mathematics
Publisher
International Press of Boston, Inc.
Citation
Lusztig, George. "On Some Partitions of a Flag Manifold." Asian J. Math. 15.1 (2011): 1--8.
Version
Original manuscript
Abstract
Let G be a connected reductive group over an algebraically closed field k of characteristic p ≥ 0. Let W be the Weyl group of G. Let W be the set of conjugacy classes in W. The main purpose of this paper is to give a (partly conjectural) definition of a surjective map from W to the set of unipotent classes in G (see 1.2(b)). When p = 0, a map in the opposite direction was defined in [KL, 9.1] and we expect that it is a one sided inverse of the map in the present paper. The (conjectural) definition of our map is based on the study of certain subvarieties B[w over g] (see below) of the flag manifold B of G indexed by a unipotent element g ∈ G and an element w ∈ W.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
http://projecteuclid.org/euclid.ajm/1306616061
