Induced nilpotent orbits and birational geometry

Understand

In general, a nilpotent orbit closure in a complex simple Lie algebra \g, does not have a crepant resolution.

• But, it always has a Q-factorial terminalization by the minimal model program.
• According to B.
• Fu, a nilpotent orbit closure has a crepant resolution only when it is a Richardson orbit, and the resolution is obtained as a Springer map for it.