## University of Sydney Algebra Seminar

# Anthony Henderson (University of Sydney)

## Friday 28th August, 12.05-12.55pm, Carslaw 375

### Pieces of nilpotent cones for classical groups

The algebraic groups SO_{2n+1} and Sp_{2n} have dual root data, so one expects there to be close connections between them. However, the nilpotent orbits of SO{2n+1} in its Lie algebra seem superficially different from those of Sp_{2n}. Lusztig observed that on each side the orbits can be lumped together into `special pieces' which correspond more closely. For example, the number of points defined over a finite field in each special piece for SO_{2n+1} is the same as that in the corresponding special piece for Sp_{2n}, as Lusztig showed by direct computation. I will explain a new approach to this phenomenon, in which the two nilpotent cones are related via the exotic nilpotent cone of S. Kato. This is joint work with P. Achar (Louisiana State University) and E. Sommers (University of Massachusetts).