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$G$-orbits in Springer resolution (or, stabilizer actions on Springer fibers)

The question is equivalent to studying the $B$-orbits in $\mathfrak u$. Then Kashin proved that for $G$ simple the number of $B$-orbits in $\mathfrak u$ is finite iff $G$ is of type $A_n$, $n\le4$ or …
Friedrich Knop's user avatar