  The irreducible components of the variety of all modules over the
preprojective algebra and MV cycles both index bases of the universal
enveloping algebra of the positive part of a semisimple Lie algebra
canonically. To relate these two objects Baumann and Kamnitzer associate a
cycle in the affine Grassmannian for a given module. It is conjectured that the
ring of functions of the T-fixed point subscheme of the associated cycle is
isomorphic to the cohomology ring of the quiver Grassmannian of the module. I
give a proof of part of this conjecture. Given this conjecture, I give a proof
of the reduceness conjecture.
