Pursuing the double affine Grassmannian II: Convolution

This is the second paper of a series (started by Braverman and Finkelberg, 2010 [2], ) which describes a conjectural analog of the affine Grassmannian for affine Kac–Moody groups (also known as the double affine Grassmannian). The current paper is dedicated to describing a conjectural analog of the convolution diagram for the double affine Grassmannian. In the case when G=SL(n) our conjectures can be derived from Nakajima (2009) [12].