DIMENSION DES FIBRES DE SPRINGER AFFINES POUR LES GROUPES

This article establishes a dimension formula for a group version of affine Springer fibers. We follow the method initiated by Bezrukavnikov in the case of Lie algebras. It consists in the introduction of a big enough regular open subset, with the same dimension as the affine Springer fiber. We show that, in the case of groups, such a regular open subset with analogous properties exists. Its construction needs the introduction of the Vinberg semi-group V-G, for which we study an adjoint quotient chi(+) and extend for chi(+) the results previously established by Steinberg.