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In arXiv:1807.09038 we formulated a conjecture describing the derivedcategory D-mod(Gr$_{GL(n)}$) of (all) D-modules on the affine Grassmannian ofthe group $GL(n)$ as the category of quasi-coherent sheaves on a certain stack(it is explained in loc. cit. that this conjecture "follows" naturally fromsome heuristic arguments involving 3-dimensional quantum field theory). In thispaper we prove a weaker version of this conjecture for the case $n=2$.

A quasi-coherent description of the category D-mod(Gr$_{GL(n)}$)