Publication Date
2010
Abstract
We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$, and Kato's exotic nilpotent cone. We prove that the number of $\F_q$-points in each nilpotent orbit of type $B_n$ or $C_n$ 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 $B_n$ and $C_n$ have the same number of $\F_q$-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.
Recommended Citation
Achar, Promad; Henderson, Anthony; and Sommers, E, "PIECES OF NILPOTENT CONES FOR CLASSICAL GROUPS" (2010). Mathematics and Statistics Department Faculty Publication Series. 1149.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1149
Comments
This is the pre-published version harvested from ArXiv.