  This paper is the first in a series that describe a conjectural analog of the
geometric Satake isomorphism for an affine Kac-Moody group. In this paper we
construct a model for the singularities of some would-be Schubert varieties in
the affine Grassmannian for an affine Kac-Moody group. We formulate a
conjecture describing the (local) intersection cohomology of these varieties in
terms of integrable representations of the Langlands dual affine Kac-Moody
group and check this conjecture in a number of cases. Roughly speaking the
above singularities are constructed by looking at the Uhlenbeck space of
instantons on the quotient of the affine plane by a finite cyclic subgroup of
SL(2).
