The dual approach to the Springer fiber=orbital variety
Dr. Pagnon Ngoc Gioan Jean
ICTP, Trieste, Italy.
At first I will recall some results made by Steinberg and Spaltenstein, which relied some geometric properties of the Springer of type A to some well-known combinatoric rules. After I want to present the dual point view of the Springer fiber :"the orbitals varieties" which are by definition the irreducible components of the intersection between a nilpotent orbit with the nilpotent radical of the borel subalgebra. The "nice" particularity of an orbital variety is that it stable under the adjoint action of the Borel subgroup. I have adopted recently this approach, and I will give some properties about the Borel action on the nilpotent radical of is Lie algebra. In some sence this approach is very closed to the way for describing the action of the Borel in the flag manifold: a representative for every Borel orbit, (some) incidence relations...