Cluster theory of the coherent Satake category

Understand

We study the category of G(O)-equivariant perverse coherent sheaves on the affine Grassmannian of G.

• This coherent Satake category is not semisimple and its convolution product is not symmetric, in contrast with the usual constructible Satake category.
• Instead, we use the Beilinson-Drinfeld Grassmannian to construct renormalized r-matrices.
• These are canonical nonzero maps between convolution products which satisfy axioms weaker than those of a braiding.