Pieces of Nilpotent Cones for Classical Groups
نویسنده
چکیده
We compare orbits in the nilpotent cone of type Bn, that of type Cn, and Kato’s exotic nilpotent cone. We prove that the number of Fq-points in each nilpotent orbit of type Bn or Cn equals that in a corresponding union of orbits, called a type-B or type-C piece, in the exotic nilpotent cone. This is a finer version of Lusztig’s result that corresponding special pieces in types Bn and Cn have the same number of Fq-points. The proof requires studying the case of characteristic 2, where more direct connections between the three nilpotent cones can be established. We also prove that the type-B and type-C pieces of the exotic nilpotent cone are smooth in any characteristic.
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