Informal Friday Seminar: Cliff -- Beilinson-Drinfeld Grassmannian and fusion

Last semester we have seen the basics of the geometric Satake equivalence, which gives a 
geometric realization of representations of a reductive algebraic group in terms of 
perverse sheaves on the affine Grassmannian. However, the symmetry of the convolution 
product was stated and not explained. This turns out to be a significant issue that was 
solved by Drinfeld in the 80s, and not explained to anyone for about twenty years.

I will explain the key ideas behind Drinfeld’s construction. The key point is to 
"globalize" the affine Grassmannian, which first involves interpreting the affine 
Grassmannian as a moduli space of "ways of changing a G-bundle on a curve a point". Then 
nearby cycles come to the rescue!