Representations of the elliptic affine Hecke algebras

We prove that irreducible representations of the elliptic affine Hecke algebras Ginzburg, Kapranov, and Vasserot are in one-to-one correspondence with certain nilpotent Higgs bundles on curve. The main tool we use is equivariant cohomology Steinberg variety Springer resolution. As a by-product, study at roots unity type- A . another define version Demazure-Lusztig operators dynamical parameters satisfy braid relations. discuss speculative indications this 4d N = 2 gauge theory.