cherednik algebra - Quantum equivariant $K$-theory and DAHA.

My best guess is that either

1. this is true for $mathbb{CP}^1$, and it's pretty easy to generalize that given what's already in that paper, or


2. this is false for $mathbb{CP}^1$, and you're hosed.

The bit one has to understand is the map from the 2 point genus 0 moduli space to the Steinberg variety. BMO get away with just noting that the two spaces have the same dimension, so the pushforward of the fundamental class of the moduli space has to be a sum of fundamental classes of components of Steinberg, whose coefficients they work out by deforming to an almost generic situation and doing the calculation for $mathbb{CP}^1$.

I think by looking at the pushforward of the structure sheaf on the 2-point moduli space, you'll find that quantum correction is some K-class on the Steinberg variety and thus something in the affine Hecke algebra, and I think it should be the sum of SL(2) contributions for each root by the same deformation arguments that BMO use.

---

I just spoke to Davesh Maulik about this, and it seems my intuition has failed me: he claims it is just hard, and the techniques of that paper will not work.