London Algebra Colloquium abstract
Pieces of nilpotent cones for classical groups
Anthony Henderson (Sydney), 18th March 2010
Abstract
The algebraic groups SO2n+1 and Sp2n have dual root data, so one expects
there to be close connections between them. However, the nilpotent orbits
of SO2n+1 in its Lie algebra seem superficially different from those of Sp2n.
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 SO2n+1 is the same
as that in the corresponding special piece for Sp2n, 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).