  By the geometric Satake correspondence, the number of components of certain
fibres of the affine Grassmannian convolution morphism equals the tensor
product multiplicity for representations of the Langlands dual group. On the
other hand, in the case of GL_n, combinatorial objects called hives also count
tensor product multiplicities. The purpose of this paper is to give a simple
bijection between hives and the components of these fibres. In particular, we
give a description of the individual components. We also describe a conjectural
generalization involving the octahedron recurrence.
