Tonny Albert Springer

""Intersection cohomology of large Schubert varieties"

Let G be an adjoint group and X its wonderful compactification, due to De Concini and Procesi. This is a variety on which GxG acts. B denoting a Borel group of G, the group BxB has finitely many orbits in X. It is shown that the -local and global- intersection cohomology of the closure of a BxB-orbit. A particular case of such a closure is a large Schubert variety, the closure of a double coset BwB in G. A new kind of Kazhdan-Lusztig polynomials make their appearance.