This is a six hour lecture course to be given at Northeastern in the week of February 20-24.
Tuesday, Feb 21, 10am-12pm, Thursday, Feb 23, 2-4pm, Friday, Feb 24, 10am-12pm. All three lectures are in WVF 010 (WVF is building 23F on this map)
Title: Introduction to affine Grassmannians and the geometric Satake equivalence.
Abstract: The goal of these lectures will be to start from scratch and learn what the affine Grassmannian of a reductive group is, and how its geometry is related to the representation theory of reductive groups. I will emphasize the examples of GL_n and SL_2 throughout.
Here is a rough outline of the three lectures:
Lecture 1: definitions; lattice model for GL_n; orbits.
Lecture 2: convolution product; Lusztig's q-analogue of the weight multiplicity; geometric Satake equivalence.
Lecture 3: Iwahori orbits; Finkelberg-Mirkovic conjecture; Koszul duality.
Notes for lecture 1.
Notes for lecture 2.
Notes for lecture 3.
All notes are taken by Jose Simental.