⇤Math diary
May 26, 2023:
Today I read part of chapter 8 of Pressley-Segal’s book “Loop groups”. This is about the affine grassmanian and other important homogenous spaces on loop groups. I needed this because I want to learn about Borel-Bott-Weil on loop groups, which has to do with line bundles on this space (chapter 11). This gives a global, geometric, uniform way of constructing the desired representations of loop groups. I want the borel-bott-weil story so that I can understand the BGG resolution on loop spaces, which is at the end of chapter 14. I’m getting there.