The xi-stability on the affine grassmannian

We introduce a notion of xi-stability on the affine grassmannian (SIC) for the classical groups, this is the local version of the xi-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient (SIC)(xi)/T of the stable part (SIC)(xi) by the maximal torus T exists as an ind-k-scheme, and we introduce a reduction process analogous to the Harder-Narasimhan reduction for vector bundles over an algebraic curve. For the group , we calculate the Poincar, series of the quotient (SIC)(xi)/T.