Let H be a connected reductive group over an algebraically closed field. We define a surjective map from the set of character sheaves on H (up to isomorphism) to the set of strata of H. To do this we use the generalized Springer correspondence.
Unipotent character sheaves and strata of a reductive group, II
A Partial Order on Bipartions From the Generalized Springer Correspondence
Generalized Springer correspondence for symmetric spaces associated to orthogonal groups
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