Type: Seminar

Distribution: World

Expiry: 28 Feb 2021

CalTitle1: Cliff - Beilinson-Drinfeld Grassmannian and fusion

Calendar2: 13 Mar 2020 1500-1700

CalLoc2: Quad S224

CalTitle2: Cliff - Beilinson-Drinfeld Grassmannian and fusion

Auth: romanova@203.54.33.225 (arom8272) in SMS-WASM

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!