On Some Partitions of a Flag Manifold
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Asian Journal of Mathematics
International Press of Boston, Inc.
Lusztig, George. "On Some Partitions of a Flag Manifold." Asian J. Math. 15.1 (2011): 1--8.