Abstract
Let $G$ be a connected reductive algebraic group over an algebraic closure of a finite field of characteristic $p$. Under the assumption that $p$ is good for $G$, we prove that for each character sheaf $A$ on $G$ which has non-zero restriction to the unipotent variety of $G$, 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 $G$ on which $A$ has non-zero restriction has dimension strictly smaller than that of $C_A$.
Citation
Anne-Marie Aubert. "Character sheaves and generalized Springer correspondence." Nagoya Math. J. 170 47 - 72, 2003.
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