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We compare orbits in the nilpotent cone of type B , that of type C , and Kato’s exotic nilpotent cone. We prove that the number of F -points in each nilpotent orbit of type B or C 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 where corresponding special pieces in types B and C have the same number of F -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. © 2011 American Mathematical Society. n n q n n n n q

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Representation Theory

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