The real affine Grassmannian and quantum SL(2)
The real affine Grassmannian and quantum SL(2)
We prove that a certain full subcategory of equivariant perverse sheaves on the affine Grassmannian of PGL(2, R) is equivalent to representations of Lusztig's quantum SL(2) at a primitive fourth root of unity. Nadler's functor of nearby cycles from the complex affine Grassmannian corresponds to quantum Frobenius.