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Dec 30, 2013 at 13:32 comment added Peter Crooks I think the relationship may be more extensive, but I am not sure. I believe that Pressley and Segal introduced a differential-geometric notion of the affine Grassmannian. This version of the affine Grassmannian is more explicitly related to the finite-dimensional case. The trick is then to relate the Pressley-Segal version of the affine Grassmannian to $Gr_G$ when $G$ is a complex reductive group.
Dec 30, 2013 at 13:15 history answered abx CC BY-SA 3.0