Nombres de Betti des fibres de Springer de type A

Abstract

Let u be a nilpotent endomorphism of a finite dimensional vector space. The Springer fiber over u, denoted by B u , is the variety of complete flags stable by u. We determine the Betti numbers of B u . To do this, we construct a cell decomposition of B u . The codimension of the cells is similar to a Coxeter length, this makes our cell decomposition well suited for the calculation of Betti numbers. To cite this article: L. Fresse, C. R. Acad. Sci. Paris, Ser. I 347 (2009).