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This is the third paper of a series (started by arXiv:0711.2083,arXiv:0908.3390) which describes a conjectural analog of the affineGrassmannian for affine Kac-Moody groups (also known as the double affineGrassmannian). The current paper is dedicated to describing a conjecturalanalog of the convolution diagram for the double affine Grassmannian and affineZastava.

Pursuing the double affine Grassmannian III: Convolution with affine Zastava