The past few weeks there has been a summer school and conference on geometric representation theory and extended affine Lie algebras at University of Ottawa. As part of this event, I gave a week long lecture series entitled “three geometric constructions of the irreducible representations of “. Specifically I discussed the Borel-Weil theorem, Ginzburg’s construction using Springer fibres, and the geometric Satake correspondence. I focused on to keep the root system combinatorics and the geometry as elementary as possible.
The other lectures at the summer school were given by Neher, Kang, Wang, Savage, and Chari. I recommend reading their notes/watching their videos if you want to learn more about geometric representation theory, crystals, and affine Lie algebras.