Abstract: We will deduce the Kazhdan–Lusztig isomorphism from explicitly working out the $\mathrm{SL}_2$ case and bootstrapping this case to compare the action of $K^{G \times \mathbb{G}_m}(\Tilde{N} \otimes_N \Tilde{N})$ on $K^{G \times \mathbb{G}_m}(\Tilde{N}) $with the anti-spherical module of the Iwahori-Hecke algebra. Along the way we will perform equivariant cohomology calculations on pieces of the Steinberg variety and discuss Borel-Weil-Bott.

Seminar webpage: https://umrep.github.io/