Chen, Zongbin2015-09-282015-09-282015-09-28201510.1007/s00209-015-1471-2https://infoscience.epfl.ch/handle/20.500.14299/118867WOS:000358208300031We 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.text::journal::journal article::research article