Satake Equivalence

Organizers: Runlei Xiao, Khai-Hoan Nguyen-Dang

Time: The seminar will be held on Friday, room (TBA), from 14:00. The first talk will take place on November 24

Goal: The first part of the seminar will focus on the affine Grassmannians.
The second part of the seminar will introduce the geometric Satake equivalence.

We mainly follow the lecture notes by Xinwen Zhu.

An outline for the seminar can be found here.

Tentative Schedule

Talk I: [Zhu16][1.1] - November 24, room 2AB40, 13:30-14:30

• Introduce the functor point of view 

Introduce the usual Grassmannians, and prove that they are projective schemes

Briefly disscuss about the affine Grassmannians.

Speaker: Runlei Xiao

Talk II: [Zhu16][1.2, 1.3] December 1, room 2AB40, 14:00-15:00

• Explain the notion of ind-scheme, and the theorem states that the affine

Grassmannian is represented by an ind-projective scheme.

Introduce the affine Grassmannians of general groups.

• Introduce jet and loop groups and their properties.

Speaker: Khai-Hoan Nguyen-Dang

Talk III: [Zhu16][1.5, 1.6, 1.7]

• Discuss the moduli interpretation of Grassmannian due to Beauville-Laszlo.

• Examine the affine Grassmannians over complex numbers.

• Examine the affine Grassmannian over p-adic fields.

Speaker: Runlei Xiao

Talk IV: [Zhu16][2.1]

• Introduce Schubert varieties and Schubert cells

Speaker: Khai-Hoan Nguyen-Dang

Talk V: [Zhu16][3.1, 3.2]

• Beilinson-Drinfeld Grassmannians

• Factorization theorem


Talk VI: [Zhu16][Appendix A.1 , 5.1]

• Perverse Sheaf

• Satake catgory


Talk VII: [Zhu16][5.2]

• Tannakian category

• Satake as Tannakian category


Talk VIII: [Zhu16][5.3, 5.4]

• Langlands dual group

• Fusion product


Talk IX: [Zhu16][5.5, 5.6]

• Geometric Satake Isomorphism

• Relation with classical Satake isomorphism