Equivariant (k-)homology of Affine Grassmannian and Toda Lattice

1.1. Let G be an almost simple complex algebraic group, and let GrG be its affine Grassmannian. Recall that if we set O = C[[t]], F = C((t)), then GrG = G(F)/G(O). The equivariant cohomology ring H• G(O)(GrG, C) = H • G(O)(GrG) was computed by V. Ginzburg [7] in terms of the Langlands dual group Ǧ. More precisely, let ǧ be the Lie algebra of Ǧ, and let Z… (More)