Geometric Satake equivalence

主讲人 Speaker:Yuval Flicker
时间 Time: 每周二、周四09:50-11:25,2019-9-24 ~ 10-24
地点 Venue:清华大学宁斋W11

课程描述 Description

We shall introduce the affine Grassmanian Gr of a reductive connected algebraic group G over C, the category of spherical perverse sheaves on Gr, a convolution product on these sheaves, and use the Tannakian formalism to show that this category is equivalent to that of finite dimensional complex representations of the dual group of G. This is a first step in Drinfeld's ``geometric Langlands program". In fact these lectures would attempt to understand the terms mentioned here, outline some proofs and constructions, and perhaps get to some applications.

预备知识 Prerequisites

Some basic algebra, such as algebraic groups, sheaves.

参考资料 References

I. Mirkovic, K. Vilonen. Geometric Langlands duality and representations of algebraic groups over commutative rings. Annals of Math. 166 (2007), 95-143.