  We explain (following V. Drinfeld) how the equivariant derived category of
the affine Grassmannian can be described in terms of coherent sheaves on the
Langlands dual Lie algebra equivariant with respect to the adjoint action, due
to some old results of V. Ginzburg. The global cohomology functor corresponds
under this identification to restricti on to the Kostant slice. We extend this
description to loop rotation equivariant derived category, linking it to
Harish-Chandra bimodules for the Langlands dual Lie algebra, so that the global
cohomology functor corresponds to the quantum Kostant-Whittaker reduction of a
Harish-Chandra bimodule. We derive a conjecture from math.AG/0306413 which
identifies the loop-rotation equivariant homology of the affine Grassmannian
with quantized completed Toda lattice.
