Character Sheaves and Generalized Springercorrespondenceanne - Marie

Let G be a connected reductive algebraic group over an algebraic closure of a nite eld of characteristic p. Under the assumption that p is good for G, we prove that for any character sheaf A on G, there exists a unipotent class C A canonically attached to A, such that A has non-zero restriction on C A , and any unipotent class C in G such that A has non-zero restriction on C has dimension strictly smaller than that of C A. When G is of classical type, and the family of representations of the Weyl group of G associated with A is cuspidal, we prove that C is contained in the Zariski closure of C A .